Answer:
Mn2+(aq) + 2H2O(l) ⇒ MnO2(s) + 4H+(aq) + 2e-
Explanation:
Step 1: Data given
The oxidation number of manganese ion (Mn2+ ) is +2
The oxidation number of manganese dioxide is +(MnO2)4
This means the oxidation number from Mn will go from +2 to +4, since it's increased, this is an oxidation reaction
Mn2+(aq) ⇒ MnO2(s)
We have to balance both sides. Mn is already the same. But on the right side we have O atoms. T obalance both sides we have to add O atoms to the left side. This by adding 2x H2O
Mn2+(aq) + 2H2O(l) ⇒ MnO2(s)
Now the amount of O atoms is balanced, but we have H- atoms at the left side. To balance we have to add 4 H atoms to the right side
Mn2+(aq) + 2H2O(l) ⇒ MnO2(s) + 4H+(aq)
Now the amount of atoms is balanced at both sides. We also have to check if the charge on both sides is the same.
Since the left side has a charge of +2, and right has a charge of +4, we have to add 2 electrons to balance this.
Mn2+(aq) + 2H2O(l) ⇒ MnO2(s) + 4H+(aq) + 2e-
Question 4
18 g of carbon dioxide contains how many oxygen atoms?
Answer:
4.92×10²³ atoms of oxygen.
Explanation:
We'll begin by calculating the number of mole of oxygen in 1 mole of CO₂. This can be obtained as follow:
1 mole of CO₂ contains 2 mole of oxygen.
1 mole of CO₂ = 12 + (2×16)
= 12 + 32
= 44 g
Thus,
44 g of CO₂ contains 2 moles of oxygen.
Next, we shall determine the number of mole of oxygen in 18 g of CO₂. This can be obtained as follow:
44 g of CO₂ contains 2 moles of oxygen.
Therefore, 18 g of CO₂ will contain
= (18 × 2)/ 44 = 0.818 mole of oxygen.
Finally, we shall determine the number of atoms in 0.818 mole of oxygen. This can be obtained as follow:
From Avogadro's hypothesis,
1 mole = 6.02×10²³ atoms.
Therefore,
0.818 mole = 0.818 × 6.02×10²³ atoms.
0.818 mole of oxygen = 4.92×10²³ atoms.
Thus, 18 g of CO₂ contains 4.92×10²³ atoms of oxygen.
When 1 mole of CO(g) reacts with H2O(l) to form CO2(g) and H2(g) according to the following equation, 2.80 kJ of energy are absorbed. CO(g) + H2O(l)CO2(g) + H2(g) Is this reaction endothermic or exothermic? _________ What is the value of q? kJ
What volume of 1.50 mol/L stock solution is needed to make 125 mL of 0.60 mol/L solution?
Chemistry 11 Solutions
978Ͳ0Ͳ07Ͳ105107Ͳ1Chapter 8 Solutions and Their Properties • MHR | 85
Amount in moles, n, of the NaCl(s):
NaCl
2.5 g
m
n
M
58.44 g
2
4.2778 10 m l
ol
o
/m
u
Molar concentration, c, of the NaCl(aq):
–2 4.2778 × 10 mol
0.100
0.42778 mol/L
0.43 mol
L
/L
n
c
V
The molar concentration of the saline solution is 0.43 mol/L.
Check Your Solution
The units are correct and the answer correctly shows two significant digits. The
dilution of the original concentrated solution is correct and the change to mol/L
seems reasonable.
Section 8.4 Preparing Solutions in the Laboratory
Solutions for Practice Problems
Student Edition page 386
51. Practice Problem (page 386)
Suppose that you are given a stock solution of 1.50 mol/L ammonium sulfate,
(NH4)2SO4(aq).
What volume of the stock solution do you need to use to prepare each of the
following solutions?
a. 50.0 mL of 1.00 mol/L (NH4)2SO4(aq)
b. 2 × 102 mL of 0.800 mol/L (NH4)2SO4(aq)
c. 250 mL of 0.300 mol/L NH4
+
(aq)
What Is Required?
You need to calculate the initial volume, V1, of (NH4)2SO4(aq) stock solution
needed to prepare each given dilute solution.
The dilution gives the relationship between the molarity and the volume of the solution. The volume of stock solution with a molarity of 1.50 mol/L is 50 mL.
What is dilution?Dilution is said to be the addition of more volume to the concentrated solution to make it less in molar concentration. This tells about the inverse and indirect relationship between the volume and the molar concentration of the solution.
Given,
Initial volume = V₁
Initial molar concentration (M₁) = 1.50 mol/L
Final volume (V₂) = 125 mL = 0.125 L
Final molar concentration (M₂)= 0.60 mol/L
The dilution is calculated as:
M₁V₁ = M₂V₂
V₁ = M₂V₂ ÷ M₁
Substituting the values in the above formula as
V₁ = M₂V₂ ÷ M₁
V₁ = (0.60 mol/L × 0.125 L) ÷ 1.50 mol/ L
V₁ = 0.05 L
= 50 mL
Therefore, 50 mL of stock solution is needed to make a 0.60 mol/L solution.
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When would exposure to a potentially harmful substance most likely to damage many organs in a developing embryo?
A wavelength of 489.2 nm is observed in a hydrogen spectrum for a transition that ends in the nf level of the Balmer series. What was ni for the initial level of the electron
Answer:
[tex]n_1=4[/tex]
Explanation:
From the question we are told that:
Wavelength [tex]\lambda=489.2 nm =>4.86*10^{-7}[/tex]
nf level= Balmer series
nf level= 2
Generally the equation for Wavelength is mathematically given by
[tex]\frac{1}{\lambda}=R[\frac{1}{nf^2}-\frac{1}{n_1^2}][/tex]
Where
[tex]R=Rydberg Constant[/tex]
[tex]R=1.097*10^7[/tex]
Therefore
[tex]\frac{1}{4.86*10^{-7}}=1.097*10^7[\frac{1}{2^2}-\frac{1}{n_1^2}][/tex]
[tex]n_1=4.0021[/tex]
[tex]n_1=4[/tex]
why is it difficult to undergo nucleophilic substitution in haloarene?
Answer:
In Haloarenes the C atom to which the X group is attached is SP2 hybridized thus it is become difficult to replace it by the Nucleophile. Since arenes and Vinyl halides are electron rich molecules due to presenceof n bonds, they repel Nucleophile attacking them.
Question:-
Why it is difficult for haloarenes to undergo nucleoplhilic subsituⁿ reaction?
Answer:-
Haloarenes are less reactive towards the nucleoplhilic substitution rxⁿ . This is due to following reasons :-
[tex]\red{\bigstar}\underline{\textsf{ Reason 1 :- Partial double bond character .}}[/tex]
Halogen atom has one lone pair, and due to presence of π - σ - lp , resonance is established in the compound ( see attachment) . Due to resonance there is a partial double bond character in the carbon halogen bond , so it is difficult to break a double bond than a single bond.
[tex]\rule{200}2[/tex]
[tex]\red{\bigstar}\underline{\textsf{ Reason 2 :- $\pi$ cloud .}}[/tex]
When a nucleoplhile comes to attack , it is repelled by the π-cloud of the benzene ring.
[tex]\rule{200}2[/tex]
[tex]\red{\bigstar}\underline{\textsf{ Reason 3 :- Phenyl cation .}}[/tex]
If somehow the halogen atoms leaves the benzene ring ,being more electronegative than carbon , it takes away the electron , thus a positive charge is left on benzene ring and the phenyl cation so formed is very unstable .
[tex]\rule{200}2[/tex]
Hypercalcemia sign and symptoms severe symptoms
Answer:
Hypercalcemia can cause stomach upset, nausea, vomiting and constipation. Bones and muscles. In most cases, the excess calcium in your blood was leached from your bones, which weakens them. This can cause bone pain and muscle weakness.
Some symptoms are:
Fatigue, bone pain, headaches.
Nausea, vomiting, constipation, decrease in appetite.
Forgetfulness.
Lethargy, depression, memory loss or irritability.
Muscle aches, weakness, cramping and/or twitches.
Suppose you are using distillation to separate cyclohexane and toluene. The boiling point of cyclohexane is Choose... oC and the boiling point of toluene is Choose... oC. Therefore, the liquid collected first should be Choose... .
Answer:
81°C
111°C
cyclohexane
Explanation:
Distillation is a process of separating two liquids based on differences in Bolling point. For two substances having different boiling points, they are collected as they are converted into vapour, condensed and move down the condenser one after the other.
Since the boiling point of cyclohexane is less than that of toluene, cyclohexane is collected first before toluene.
A tank contains isoflurane, an inhaled anesthetic, at a pressure of 0.30 atm and 17.9°C. What is the pressure, in atmospheres, if the gas is warmed to a
temperature of 27.4°C, if n and V do not change?
Explanation:
here's the answer to your question
The pressure of the isoflurane gas at the temperature of 27.4 °C is 0.31 atm.
What is Gay Lussac's law?Gay-Lussac's law states that the pressure of a gas is directly proportional to the absolute temperature when the volume of the gas is kept constant.
Mathematically, Gay Lussca's law can be written as follows:
P/T = k
It is also expressed as the pressure of the gas being directly proportional to temperature.
P ∝ T (where V is constant)
or
[tex]\frac{P_1}{T_1} =\frac{P_2}{T_2}[/tex] ................(1)
Given, the initial pressure and initial temperature of the gas:
P₁ = 0.30 atm
and T₁ = 17.9 °C. = 17.9 + 273 = 290.9 K
The final temperature of gas T₂ = 27.4°C = 27.4 + 273 = 300.4 K
Now, from the equation (1): [tex]P_2=\frac{P_1\times T_2}{T_1}[/tex]
P₂ = (0.30) × (300.4)/290.0
P₂ = 0.31 atm
Therefore, the pressure of the isoflurane at 27.4°C is equal to 0.31 atm.
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# of protons
# of neutrons
# of electrons
Atomic Number
Mass Number
18
17
35
17
37
6
8
6
6
15
Answer:
35
Explanation:
is the answer for your question
A 10.53 mol sample of krypton gas is maintained in a 0.8006 L container at 299.8 K. What is the pressure in atm calculated using the
van der Waals' equation for Kr gas under these conditions? For Kr, a = 2.318 L'atm/mol and b = 3.978x10²L/mol.
Answer:
-401.06 atm
Explanation:
Applying,
P = (nRT/V-nb)-(an²/V²)............... Equation 1
Where P = Pressure, R = Universal gas constant, V = molar Volume, T = Temperature in Kelvin, a = gas constant a , b = gas constant b, n = numbers of mole
From the question,
Given: T = 299.8 K, V = 0.8006 L, a = 2.318 L.atm/mol, b = 3.978×10²L/mol
Constant: R = 0.0082 atm.dm³/K.mol
Substitute these values into equation 1
P = [(0.0082×299.8×10.53)/(0.8006-(10.53×397.8)]-[(10.53²×2.318/0.8006²)]
P = (25.89/-4188.0334)-(400.995)
P = -0.0618-400.995
P = -401.06 atm
Which process refers to the dissociation of Naci into Na+ and Ci+?
Answer:
dissolution is the process
Critique this statement: Promotion of electrons is accompanied by a release of energy
Answer: Promotion of electrons is accompanied by a release of energy because of absorption of photon.
Explanation:
Promotion of electrons occurs when an electron accepts or absorbs a photon which leads to it's movement from a lower energy level orbital to a higher energy orbital.
According to Bohr, the electrons was restricted to certain energy levels and was thought to move along certain circular orbits around the nucleus. These energy levels were identified by means of principal quantum number, n. The wave mechanics model of atom does not restrict the electrons to a certain energy levels only. Instead it describes a region around the Nucleus called orbitals where there is a possibility of finding an electron with a certain amount of ENERGY.
The energy levels are composed of one or more orbitals and the distribution of electrons around the nucleus is determined by the number and kind of energy levels that are occupied.
Bohr made an assumption that an electron emits energy in the form of radiation when it moves from a higher to a lower permitted orbit, this produces a line in the atomic emission spectrum. Since the energies of the higher and lower orbits are fixed, the line will be of a particular energy and frequency.
If 50.0 g of sulfuric acid and 40.0 grams of barium chloride are mixed, how many grams of sulfuric acid and how many grams of barium chloride remain after the double replacement reaction is complete?
After the double replacement reaction from mixing 50.0g of sulfuric acid and 40.0 grams of barium chloride is complete, 31.16 grams of sulfuric acid and 0 grams of barium chloride remain.
The equation of the reaction between sulfuric acid and barium chloride is
BaCl₂ + H₂SO₄ → BaSO₄ + 2HCl
From this equation of reaction, it means 1 mole of barium chloride will completely react with 1 mole of sulfuric acid.
From the question, we have 50.0g of sulfuric acid and 40.0 grams of barium chloride.
First, we will determine the number of moles of the sulfuric acid and barium chloride present.
Number of moles is given by the formula
Number of moles = Mass / Molar mass
For sulfuric acid
Mass = 50.0 g
Molar mass = 98.079 g/mol
∴ Number of moles = 50.0 / 98.079
Numbers of moles of sulfuric = 0.509793 mol
For barium chloride
Mass = 40.0 grams
Molar mass of barium chloride = 208.23 g/mol
∴ Number of moles = 40.0 / 208.23
Number of moles of barium chloride = 0.192095 mol
Since the number of moles of sulfuric acid is more than that of barium chloride, then the limiting reagent is barium chloride and the excess reagent is sulfuric acid
NOTE: A limiting reagent is the reactant that is completely used up in a reaction, and it determines when the reaction stops.
Hence, barium chloride will be used up during the reaction (that is, 0 grams will remain after the reaction is complete).
For the mass of sulfuric acid that will remain,
First, we will determine the number of mole that will remain.
Since 1 mole of barium chloride completely reacts with 1 mole of sulfuric acid, then 0.192095 mol of barium chloride will react with 0.192095 mol of sulfuric acid.
∴ The remaining number moles of sulfuric acid = 0.509793 mol - 0.192095 mol
The remaining number moles of sulfuric acid = 0.317698 mol
Then, from
Mass = Number of moles × Molar mass
Mass = 0.317698 mol ×98.079 g/mol
Mass = 31. 1595 gram
Mass ≅ 31.16 grams
∴ 31.16 grams remains after the reaction is complete.
Hence, 31.16 grams of sulfuric acid and 0 grams of barium chloride remain after the double replacement reaction is complete.
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If the Ksp of NaCl is experimentally determined to be 43.9, then what is the concentration of Na (in M) when it begins to crystallize out of solution
Answer:
6.63 M
Explanation:
NaCl(s) ---> Na^+(aq) + Cl^-(aq)
Given that [Na^+] = [Cl^-] = s
Where s= concentration of the both ions
Ksp = s^2
s= √Ksp
s= √43.9
s= 6.63 M
The concentration of Na (in M) obtained when it begins to crystallize out of solution is 6.63 M
What is solubility of product?The solubility of product (Ksp) is defined as the concentration of products raised to their coefficient coefficients. This is illustrated below:
mX <=> nY + eZ
Ksp = [Y]^n × [Z]^e
Dissociation equationNaCl(aq) → Na⁺(aq) + Cl¯(aq)
Let the concentration of Na⁺ be yLet the concentration of Cl¯ be yHow to determine the concentration of Na⁺ Solubility of product (Ksp) = 43.9Concentration of Cl¯ = yConcentration of Na⁺ = y =?Ksp = [Na⁺] × [Cl¯]
43.9 = y × y
43.9 = y²
Take the square root of both side
y = √43.9
y = 6.63 M
Thus, the concentration of Na⁺ is 6.63 M
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explain in details how triacylglycerol have an advantage over carbohydrates as stored fuel
Answer:
As stored fuels, triacylglycerols have two significant advantages over polysaccharides such as glycogen and starch. The carbon atoms of fatty acids are more reduced than those of sugars, and oxidation of triacylglycerols yields more than twice as much energy, gram for gram, as that of carbohydrates.
Explanation:
A solution is made by dissolving 0.565 g of potassium nitrate in enough water to make up 250. mL of solution. What is the molarity of this solution?
Please explain and show work.
[tex]\\ \large\sf\longmapsto KNO_3[/tex]
[tex]\\ \large\sf\longmapsto 39u+14u+3(16u)[/tex]
[tex]\\ \large\sf\longmapsto 53u+48u[/tex]
[tex]\\ \large\sf\longmapsto 101u[/tex]
[tex]\\ \large\sf\longmapsto 101g/mol[/tex]
Now
[tex]\boxed{\sf No\:of\:moles=\dfrac{Given\:mass}{Molar\:mass}}[/tex]
[tex]\\ \large\sf\longmapsto No\:of\:moles=\dfrac{0.565}{101}[/tex]
[tex]\\ \large\sf\longmapsto No\:of\:moles=0.005mol[/tex]
We know
[tex]\boxed{\sf Molarity=\dfrac{Moles\:of\:solute}{Vol\:of\:Solution\:in\:L}}[/tex]
[tex]\\ \large\sf\longmapsto Molarity=\dfrac{0.005}{\dfrac{250}{1000}L}[/tex]
[tex]\\ \large\sf\longmapsto Molarity=\dfrac{0.005}{0.250}[/tex]
[tex]\\ \large\sf\longmapsto Molarity=0.02M[/tex]
[tex] \: \: \: \: \: \: \: \: \: [/tex]
what is the functions of sodium chloride oxalate in blood sample container
Answer:
To prevent the coagulation of blood
Explanation:
Sodium chloride oxalate in blood sample containers exists to prevent the coagulation of blood samples being collected (for analytical purposes).
The compound works by chelating or combining with blood's calcium which is necessary for blood to coagulate (change from flowing liquid to gel-like substance).
Calcium ions are known to be responsible for the activation of certain coagulation factors such as FXIII and therefore, play important roles in homeostasis during blood clotting. Hence, the removal of the calcium in blood disrupts the homeostatic process of clotting formation and results in the blood not being able to coagulate.
Complete and balance the nuclear equations for the following fission reactions.
a. 23592U+10n→16062Sm+7230Zn+?10n. Express your answer as a nuclear equation.
b. 23994Pu+10n→14458Ce+?+210n
Answer:
23592U+10n→14454Xe+9038Sr+210n
Explanation:
a nuclear reaction for the neutron-induced fission of U−235 to form Xe−144 and Sr−90.
Are the components of a solution fixed?
Answer:
yes
Explanation:
the components of solutions fixed
Part A
When the following liquids are poured into the same container, they separate as shown in the image. Based on the data
in the table below, what caused the order of the layers?
rubbing alcohol
vegetable oil
water
corn syrup
Mass
Liquid
corn syrup
water
Volume Used
95 cm
90 cm
85 cm
105 cm?
130.158
90.00 8
77.358
81.908
Density
1.37 g/cm
1 g/cm
0.91 g/cm
0.78 g/cm
vegetable oil
rubbing alcohol
I
B
X
Font Sizes
A- A -
E 3
Answer: The layers are ordered by density, with the least dense layer on top, and the densest layer on the bottom.
Explanation:
Plato
g aqueous barium hydroxide (ba(oh)2) and nitric acid (hno3) participate in a complete neutralization reaction. in the molecular equation, what are the products
Answer:
Where the products are H2O and Ba(NO3)2
Explanation:
A base, as, barium hydroxide (Ba(OH)2) reacts with an acid (HNO3), producing water (H2O), and the related salt (Ba(NO3)2) in a reaction called neutralization reaction.
The balanced reaction is:
Ba(OH)2 + 2 HNO3 → 2 H2O + Ba(NO3)2
Where the products are H2O and Ba(NO3)2
Consider the preparation of methyl benzoate by reacting benzoic acid with methanol using sulfuric acid as a catalyst. Reaction scheme of benzoic acid with methanol, conc. sulfuric acid, and heat over the arrow, and methyl benzoate and water as products. Calculate the molar masses of the reactant and product. Report molar masses to 1 decimal place. Molar mass of benzoic acid g/mol Molar mass of methyl benzoate
Answer:
See explanation
Explanation:
The molecular mass is the sum of the relative atomic masses of all the atoms in the molecule.
The relative atomic mass of reactants and products are calculated as follows;
Benzoic acid is C7H6O2 hence the molar mass of benzoic acid is ;
7(12) + 6(1) + 2(16) = 84 + 6 + 32 = 122.0 g/mol
Methyl benzoate is C8H8O2
8(12) + 8(1) + 2(16) = 96 + 8 + 32 = 136.0 g/mol
A sample of gas contains 0.1500 mol of CH4(g) and 0.1500 mol of H2O(g) and occupies a volume of 13.0 L. The following reaction
takes place:
CH_(g) + H2O(g) 3H2(g) + CO(g)
Calculate the volume of the sample after the reaction takes place, assuming that the temperature and the pressure remain constant.
L
Answer:
26.0L is the volume of the sample after the reaction
Explanation:
Based on the reaction, 1 mole of CH4 reacts with 1 mole of H2O to produce 1 mole of CO and 3 moles of H2.
That is, 1 mole of each reactant produce 4 moles of gases
As in the reaction, 0.1500 moles of CH4 and 0.1500 moles of H2O are added, 0.1500 moles of CO and 0.4500 moles of H2 are produced.
Before the reaction, the moles of gas are 0.3000 moles and after the reaction the moles are 0.6000 moles of gas.
Based on Avogadro's law, the moles of a gas are directly proportional to the volume under temperatura and pressure constant. The equation is:
V1/n1 = V2/n2
Where V is volume and n are moles of 1, initial state and 2, final state.
Replacing:
V1 = 13.0L
n1 = 0.3000 moles
V2 = ?
n2 = 0.6000 moles
13.0L*0.6000 moles / 0.3000 moles = V2
V2 = 26.0L is the volume of the sample after the reaction
Give the change in condition to go from a gas to a solid. Group of answer choices cool or increase pressure cool or reduce pressure increase heat or reduce pressure increase heat or increase pressure none of the above
Answer:
cool or increase pressure
Explanation:
For a gas to form solid. There must be reduced heat and pressure. The deposition of gas into solid occurs through the removal of thermal energy. The air looses thermal energy and changes into solid.Name this compound?
*Please asap*
Trả lời:3 5-dimethylheptane
Explanation:
Starting from (R)-3-methylhex-1-yne as the substrate at the center of your page, draw a reaction map showing the regiochemical and stereochemical outcome or outcomes for each of the following series of reagents. Name each of your products, including stereochemical designations for any chirality centers that are generated.
a. HgSO4, H2SO4, H2O
b. 1. 9-BBN; 2. H2O2, NaOH
c. Br2, CCl4
d. HBr
Solution :
A substrate is defined as the chemical species that are being observed in the chemical reaction where the substrate reacts with a reagent and forms a product. It can also be referred to the surface where some other chemical reactions are performed.
Stereochemistry is defined as the study of relative spatial arrangement of the atoms which forms the structure of the molecules and their respective manipulations.
In the context, the products including the stereochemical designations for any chirality centers starting from the (R)-3-methylhex-1-yne as the substrate are attached below.
In order to complete the reaction of hexyl magnesium bromide with acetone, what next step needs to be done.
a. Fractional Distillation.
b. Vacuum filtration.
c. Aqueous workup.
d. Crystallization.
Answer:
Aqueous workup.
Explanation:
The reaction of hexyl magnesium bromide with acetone yields a tertiary alcohol. There is an organic phase and an aqueous phase.
Aqueous workup is the process of recovering the pure tertiary alcohol from the organic phase of the system.
Hence, in order to complete the reaction of hexyl magnesium bromide with acetone, aqueous workup is required.
A alkaloid compound contains 74.02% C, 8.710% H and 17.27% N. The empirical formula of the compound is___.
If 40.57 grams of it contains 0.2500 moles, then it's molecular formula will be:______.
C₁₀H₁₄N₂ is the empirical formula of the compound whose mass is 40.57 present in 0.2500 moles.
What are alkaloid compounds?Alkaloid compounds are those naturally present organic compounds in which nitrogen is present.
First we calculate the molecular mass of wanted compound by using the below formula:
n = W/M, where
n = no. of moles = 0.2500 moles (given)
W = given mass = 40.57 grams (given)
M = molar mass = 40.57 grams/= 0.2500 moles = 162.28 g/mole
In the question, given that:
% composition of carbon = 74.02%
% composition of hydrogen = 8.710%
% composition of nitrogen = 17.27%
Now we calculate the mass of these composition by using the below formula:
Composition mass = compound mass * % composition / 100
Mass of carbon = 162.28 * 74.02 / 100 = 120.11g
Mass of hydrogen = 162.28 * 8.710 / 100 = 14.13g
Mass of nitrogen = 162.28 * 17.27 / 100 = 28.02g
Now we calculate the moles of these composition to made empirical formula as:
Moles of carbon = 120.11 / 12 = 10
Moles of hydrogen = 14.13 / 1 = 14
Moles of nitrogen = 28.02 / 14 = 2
Thus, the empirical formula of the compound is C₁₀H₁₄N₂.
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A certain watch’s luminous glow is due to zinc sulfide paint that is energized by beta particles given off by tritium, the radioactive hydrogen isotope 3 H, which has a half-life of 12.3 years. This glow has about 1/10 of its initial brightness. How many years old is the watch? g
Answer:
The watch is 40.9 years old.
Explanation:
To know how many years old is the watch we need to use the following equation:
[tex] I_{(t)} = I_{0}e^{-\lambda t} [/tex] (1)
Where:
[tex]I_{(t)}[/tex]: is the brightness in a time t = (1/10)I₀
[tex]I_{0}[/tex]: is the initial brightness
λ: is the decay constant of tritium
The decay constant is given by:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex] (2)
Where:
[tex]t_{1/2}[/tex]: is the half-life of tritium = 12.3 years
By entering equation (2) into (1) we have:
[tex] I_{(t)} = I_{0}e^{-\lambda t} = I_{0}e^{-\frac{ln(2)}{t_{1/2}}t} [/tex]
[tex] \frac{I_{(t)}}{I_{0}} = e^{-\frac{ln(2)}{t_{1/2}}t} [/tex]
By solving the above equation for "t" we have:
[tex] ln(\frac{I_{(t)}}{I_{0}}) = -\frac{ln(2)}{t_{1/2}}t [/tex]
[tex] t = -\frac{ln(\frac{I_{(t)}}{I_{0}})}{\frac{ln(2)}{t_{1/2}}} = -\frac{ln(\frac{1}{10})}{\frac{ln(2)}{12.3}} = 40.9 y [/tex]
Therefore, the watch is 40.9 years old.
I hope it helps you!
