We want to find the value of t such that the velocity vector makes an angle of 45° with both axes.
We found that:
t = (2/3)*(b/c)
The velocity vector makes an angle of 45° with the x and y axes.
We know that the position vector is:
r = r=b*t²i + c*t³j
Remember that the versor "i" corresponds to the x-component, and the versor "j" corresponds to the y-component, then:
r = r=b*t²i + c*t³j = (b*t², c*t³)
The velocity vector is the vector that we get when we differentiate the position one, remember that if:
f(x) = a*x^n
then
f'(x) = n*a*x^(n - 1)
Using this, we can find that the velocity vector is:
v = (2*b*t, 3*c*t²)
Now we want to know, when does the velocity vector make an angle of 45° with the x and y axes.
Let's think of the vector as the hypotenuse of a triangle rectangle, where the x-component is the adjacent cathetus, and the y-component is the opposite cathetus. (so the angle is measured counterclockwise from the x-axis)
We have the trigonometric equation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
So now we can replace these things with the known ones:
a = 45°
opposite cathetus = y-component = 3*c*t²
adjacent cathetus = x-component = 2*b*t
So we will get:
tan(45°) = (3*c*t²)/( 2*b*t)
1 = (3/2)*(c/b)*t
Now we can solve this for the variable, t.
1*(2/3)*(b/c) = t
t = (2/3)*(b/c)
We can conclude that at the time:
t = (2/3)*(b/c)
The velocity vector makes an angle of 45° with the x and y axes.
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explain hydrogen dioxide
Answer:
Two molecules of hydrogen combine with two molecules of oxygen to form hydrogen peroxide. Hence, its chemical formula is H2O2. It is the simplest peroxide (since it is a compound with an oxygen-oxygen single bond). Hydrogen peroxide has basic uses as an oxidizer, bleaching agent and antiseptic
5. How many moles are present in 4.20x10^24 atoms of Pb
Explanation:
[tex]57816 \: moles[/tex]
are present in 4.20x10^24 atoms of Pb
Answer:
7 moles
Explanation:
(4.2*10^24)/(6*10^23)=7
2- . the number of waves in n *10 bohr's orbit are
5. For Sodium, the Work Function is listed as 2.75 eV but the Ionization Energy is listed as 5.14 eV. Is one of the experiments wrong? Give a possible explanation as to this difference in the minimum energy needed to eject or free an electron from Sodium.
Answer:
See explanation
Explanation:
The work function of a metal is defined as that minimum energy which is required to remove one electron from the surface of a metal when it is irradiated with a photon of light. The work function is different for different metals.
The ionization energy of a metal is the energy required to remove an electron from an atom. It depends on the position of the electron within the atom.
The work function specifically refers to the energy required to remove an electron from the conduction band of a metal. Hence, the work function is always lower than the ionization energy.
Four atoms and/or ions are sketched below in accordance with their relative atomic and/or ionic radii. Which of the following sets of species are compatible with the sketch?
Explain. (a) C,Ca2+,Cl−,Br−;
(b) Sr4, Cl,Br−,Na+
(d) Al,Ra2+,Zr2+
(c) Y,K,Ca,Na+, Mg2+;
e) Fe,Rb,Co,Cs
Answer:
Hence the correct option is an option (b) Sr4, Cl,Br−,Na+.
Explanation:
Bromine and chlorine belong to an equivalent group. As we go down the group the dimensions increases which too there's a charge on the bromine atom. therefore the size of the Br- is going to be larger in comparison to the chlorine atom.
Sr atom is within the second group, and also it's below the above-mentioned atoms.so Sr is going to be the larger one among all the atoms.
Sodium and chlorine belong to an equivalent period .size decrease from left to right. but due to the charge on sodium its size decreases and there's an opportunity that Na+ size could be adequate for Cl.
Here we finally assume that two atoms are of an equivalent size (Na+ and Cl) which are less in size compared to the opposite two(Sr and Br-) during which one is greater (Sr)and the opposite is smaller(Br-).
A reaction vessel is charged with phosphorus pentachloride, which partially decomposes to phosphorus trichloride and molecular chlorine according to the following reaction:
PCl5(g)â PCl3(g)+Cl2(g)
When the system comes to equilibrium at 250.0°C, the equilibrium partial pressures are: PPCl5 = 0.688 atm and PPCl3 = PCl2 = 0.870 atm.
Required:
What is the value of Kp at this temperature?
Answer:
Kp = 1.10.
Explanation:
Hello there!
In this case, according to the given information about the chemical reaction at equilibrium, it turns out possible for us to find the partial pressures-based equilibrium expression for the decomposition of phosphorous pentachloride by applying the law of mass action whereas the pressure of products is divided by that of the reactants as shown below:
[tex]Kp=\frac{p_{PCl_3}p_{Cl_2}}{p_{PCl_5}}[/tex]
Now, we plug in the given pressures to obtain:
[tex]Kp=\frac{0.870}{0.688} \\\\Kp=1.10[/tex]
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A 25.0 mL sample of 0.150 M hypochlorous acid is titrated with a 0.150 M NaOH solution. What is the pH at the equivalence point? The Kaof hypochlorous acid is 3.0x10^-8.
a) 10.20
b) 7.00
c) 6.48
d) 7.52
e) 14.52
Answer:
pH = 10.20
Explanation:
The HClO reacts with NaOH as follows:
HClO + NaOH → H2O + NaClO
Where HClO and NaOH react in a 1:1 reaction.
As the concentration of both reactions is the same and the reaction is 1:1, to reach equivalence point are required the same 25.0mL.
And the NaClO produced decreases its concentration in 2 because the volume is doubled.
The concentration of NaClO is: 0.150M / 2 = 0.075M
The equilibrium of NaClO is:
NaClO(aq) + H2O(l) ⇄ HClO(aq) + OH-(aq)
Where Kb of reaction is 1.0x10⁻¹⁴ / Ka =
1.0x10⁻¹⁴ / 3.0x10⁻⁸ = 3.33x10⁻⁷ = [HClO] [OH-] / [NaClO]
[NaClO] = 0.075M
As both HClO and OH- comes from the same equilibrium,
[HClO] = [OH-] = X
Where X is the reactoin coordinate
Replacing:
3.33x10⁻⁷ = [X] [X] / [0.075M]
2.5x10⁻⁸ = X²
X = 1.58x10⁻⁴M = [OH-]
pOH = -log [OH-]
pOH = 3.80
pH = 14 - pOH
pH = 10.20What mass of precipitate (in g) is formed when 250.0 mL of 0.150 M CuCl₂ is mixed with excess KOH in the following chemical reaction?
CuCl₂(aq) + 2 KOH(aq) → Cu(OH)₂(s) + 2 KCl(aq)
Answer:
3.6487g
CuCl2 moles reacted = (0.15×250)/1000
according to balanced chemical equation
precipitated Cu(OH)2 moles = Reacted CuCl2 moles
molar mass of Cu(OH)2 = 63.5+ (17+1)×2 = 97.5
mass of precipitate = (97.5 × 0.15×250)/1000
= 3.648g
Carboxylic acid derivatives undergo hydrolysis to make carboxylic acids.
a. True
b. False
Answer:
TRUE
Explanation:
All carboxylic acid derivatives have in common the fact that they undergo hydrolysis (a cleav- age reaction with water) to yield carboxylic acids. with hydroxide ion to yield a carboxylate salt and an alcohol. The carboxylic acid itself is formed when a strong acid is subsequently added to the reaction mixture.
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Describe a NAMED example of a non-equilibrium system with respect to it’s energetic nature and equilibrium status.
Answer:
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of variables (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium.
Explanation:
Part A
3.75 mol of LiCl in 3.36 L of solution
Express the molarity in moles per liter to three significant figures
Answer:
1.12 mol/L.
Explanation:
From the question given above, the following data were obtained:
Mole of LiCl = 3.75 moles
Volume = 3.36 L
Molarity =?
Molarity is simply defined as the mole of solute per unit litre of the solution. Mathematically, it is expressed as:
Molarity = mole / Volume
With the above formula, we can obtain the molarity of the solution as follow:
Mole of LiCl = 3.75 moles
Volume = 3.36 L
Molarity =?
Molarity = mole /Volume
Molarity = 3.75 / 3.36
Molarity = 1.12 mol/L
Thus, the molarity of the solution is 1.12 mol/L
385 x 42.13 x 0.079 is (consider significant figures):
385 x 42.13 x 0.079 = 1281.38395
Phosphorylation of enzymes:_______.
a. always increases their activity.
b. generally occurs on Ser, Thr, and/or Tyr side chains and to a lesser extent on the His side chain.
c. is irreversible.
d. is one of only five known covalent forms of regulation.
Answer:
generally occurs on Ser, Thr, and/or Tyr side chains and to a lesser extent on the His side chain
A student has accidentally spilled 100.0 mL of 3.0 mol/L nitric acid onto the lab bench. What mass of sodium bicarbonate would the teacher need to sprinkle on this spill to neutralize and clean it up?
Answer:
25 g
Explanation:
Step 1: Write the balanced equation
HNO₃ + NaHCO₃ ⇒ NaNO₃ + H₂O + CO₂
Step 2: Calculate the reacting moles of HNO₃
100.0 mL of 3.0 mol/L HNO₃ reacted.
0.1000 L × 3.0 mol/L = 0.30 mol
Step 3: Calculate the reacting moles of NaHCO₃
The molar ratio of HNO₃ to NaHCO₃ is 1:1. The reacting moles of NaHCO₃ are 1/1 × 0.30 mol = 0.30 mol.
Step 4: Calculate the mass corresponding to 0.30 moles of NaHCO₃
The molar mass of NaHCO₃ is 84.01 g/mol.
0.30 mol × 84.01 g/mol = 25 g
Predict the missing component in the nuclear equation.
238 92U → 234 90Th + X
A. 4 2He
B. 0 -1e
C. 0 0v
Answer:
A
Explanation:
helium (alpha particle)
A Grignard reagent is prepared by reacting trans-1-bromo-1-butene with magnesium. What are the products of the reaction when this reagent is reacted with: a. Ethanol
Solution :
A Grignard compound or a Grignard reagent is defined as a chemical compound having a generic formula of R−Mg−X.
Here, X = halogen
R = organic group
The Grignard reagents are obtained by treating the organic halide with a magnesium metal.
In the context, when trans-1-bromo-1-butene is reacted with magnesium, a Grignard reagent is produced.
When this Grignard reagent is reacted with an ethanol, the following product is obtained in the attachment :
what characterizes a homogeneous mixture?
Answer:
a mixture that doesn't really show the ingredients or things put into the material or food.
A strawberry nutritional drink used for a liquid diet is flavored with methyl butanoate. Draw the structure of methyl butanoate.
Answer:
See explanation and image attached
Explanation:
Methyl butanoate is an ester. Esters have the general molecular formula, RCOOR where the two Rs may represent the same or different alkyl groups.
Methyl butanoate is has a fruity odor, smelling like apples or pineapples fragrance. It is also called methyl butyrate.
The structure of the compound is shown in the image attached to this answer.
Karl-Anthony is trying to plate gold onto his silver ring. He constructs an electrolytic cell using his ring as one of the electrodes. He runs this cell for 94.3 minutes at 205.3 mA. How many moles of electrons were transferred in this process
Answer:
0.012 moles of electrons were transferred
Explanation:
We can find the number of electrons transferred from the time in seconds and the current in Amperes using the equation:
n = I*t / F
Where n are moles of electrons transferred
I is current in Amperes = 0.2053A
t is time in seconds:
94.3min*(60s/1min) = 5658s
F is faraday constant 96485A*s/mol
Replacing:
n = 0.2053A*5658s / 96485A*s/mol
n = 0.012 moles of electrons were transferred
Moles are the mass per unit molar mass of compound. The number of moles of electrons that are transferred is 0.012 moles.
What is an electrolytic cell?An electrolytic cell is a type of electrochemical cell that uses electrical energy from external sources to conduct the chemical energy in a cell.
The moles transferred in electrolytic cells are measured as:
[tex]\rm n = \rm \dfrac{I\times t}{F}[/tex]
Given,
Current (I) in amperes = 0.2053 A
Time (t) in seconds = 5658 sec
Faraday constant (F) = 96485 A -s/mol
Substituting values in the equation above moles (n) can be calculated as:
[tex]\begin{aligned} \rm n &= \dfrac{ 0.2053 \times 5658 }{96485}\\\\&= 0.012 \;\rm mol\end{aligned}[/tex]
Therefore, 0.012 moles are transferred in this process.
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Consider a hypothetical metal that has a density of 10.6 g/cm3, an atomic weight of 176.8 g/mol, and an atomic radius of 0.130 nm. Compute the atomic packing factor if the unit cell has tetragonal symmetry, values for the a and c lattice parameters are 0.570 and 0.341, respectively.
Answer:
0.3323
Explanation:
GIven that:
Density of the metal = 10.6 g/cm^3
atomic weight = 176.8 g/mol
atmic radius = 0.130 nm
values of a and c = 0.570 nm and 0.341 nm respectively
For us to determine the atomic packing factor, we need to first determine the volume of all spheres (Vs) and the volume of unit cell (Vc).
However, the number of atoms in the unit cell (n) can be computed as:
[tex]n = \dfrac{\rho * V_c *N_A}{A} \\ \\ n = \dfrac{(10.6) * (5.7)^2 (3.41)*(10^{-24}) *(6.022*10^{23})}{176.8}[/tex]
n = 4.0
Thus, the number of atoms in the unit cell is 4
∴
The atomic paking factor (APF) is calculated by using the formula:
[tex]\dfrac{Vs}{Vc} = \dfrac{4 * \dfrac{4}{3}\pi *R^3 }{a^2 *c} \\ \\ \\ \dfrac{Vs}{Vc} = \dfrac{4 * \dfrac{4}{3}\pi *(1.30*10^{-8})^3 }{(5.70*10^{-8})^2 *(3.41*10^{-8})}[/tex]
= 0.3323
Determine whether the statement about identifying a halide is true: Regardless of any concentration of ammonium solution, the precipitates in the reaction solution of my unknown halide after 0.1M AgNO3 remain because my unknown halide solution contains Br. Select one: True False
Answer:
False
Explanation:
The statement ; Regardless of any concentration of ammonium solution the precipitate of unknown halide after 0.1M AgNO3 will remain is FALSE
This is Because the remaining concentration of AgNO3 is dependent on the solubility of Ag⁺
Which of the following chemical equations depicts a balanced ionic equation?
A. 2OH−+Ca2+−>Ca(OH)2
B. OH−+Ca2+−>Ca(OH)2
C. 2OH−+Ca2+−>2Ca(OH)2
D. OH−+2Ca2+−>Ca(OH)2
Answer:
[tex]{ \sf{A. \: 2OH {}^{ - } _{(aq)} +Ca {}^{2 + } _{(aq)} −>Ca(OH) _{2(s)} }}[/tex]
The chemical equations depict a balanced ionic equation is 2OH−+Ca2+−>Ca(OH)2. option A is correct.
What is the ionic equation?
An ionic equation is a chemical equation in which the electrolytes in an aqueous solution are expressed as dissociated ions. The ions in aqueous solutions are stabilized by ion-dipole interactions with water molecules
Strong acids, strong bases, and soluble ionic compounds (usual salts) exist as dissociated ions in an aqueous solution, and Weak acids and bases and insoluble salts are usually written using their molecular formulas because only a small amount of them dissociates into ions.
Ag+(aq) + NO3-(aq) + Na+(aq) + Cl-(aq) → AgCl(s) + Na+(aq) + NO3-(aq) is an ionic equation example.
Therefore, the balanced ionic reaction will be 2OH−+Ca2+−>Ca(OH)2. option A is correct.
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The reaction for photosynthesis producing glucose sugar and oxygen gas is:
__CO2(g) + __H2O(l) UV/chlorophyl−→−−−−−−−−−−−−−− __C6H12O6(s) + __O2(g)
What is the mass of glucose (180.18 g/mol) produced from 2.20 g of CO2 (44.01 g/mol)?
a. 66.1 g C6H12O6
b. 396 g C6H12O6
c. 54.0 g C6H12O6
d. 1.50 g C6H12O6
e. 9.01 g C6H12O6
The correct option is d.: 1.5 grams of glucose is produced from 2.20 g of CO₂.
To find the mass of glucose produced, first you must know the balanced reaction. For this, the Law of Conservation of Matter is followed.
The law of conservation of matter states that since no atom can be created or destroyed in a chemical reaction, the number of atoms that are present in the reagents has to be equal to the number of atoms present in the products.
So, in this case, the balanced reaction is:
6 CO₂ + 6 H₂O → C₆H₁₂O₆ + 6 O₂
By stoichiometry of the reaction (that is, the relationship between the amount of reagents and products in a chemical reaction), the amounts of moles of each reactant and product participate in the reaction:
CO₂: 6 moles H₂O: 6 moles C₆H₁₂O₆: 1 mole O₂: 6 molesSo, you know that 2.20 g of CO₂ react, whose molar weight is 44.01 g/mole. By definition of molar mass, 1 mole of CO₂ has 44.01 g. So, the number of moles that 2.20 grams of the compound represent is calculated as:
[tex]moles of CO_{2} =2.20 grams*\frac{1 mole}{44.01 grams}[/tex]
moles of CO₂= 0.05 moles
Now you must follow the following rule of three: if by stoichiometry of the reaction 6 moles of CO₂ produce 1 mole of C₆H₁₂O₆, 0.05 moles of CO₂ produce how many moles of C₆H₁₂O₆?
[tex]moles of C_{6} H_{12} O_{6} =\frac{0.05moles of CO_{2} *1 mole of C_{6} H_{12} O_{6}}{6moles of CO_{2}}[/tex]
moles of C₆H₁₂O₆= 8.33*10⁻³
Being the molar mass of glucose 180.18 g/mole, the mass that 8.33*10⁻³ moles of the compound represent is calculated as:
[tex]mass of glucose =8.33*10^{-3} moles*\frac{180.18 grams}{1 mole}[/tex]
mass of glucose= 1.5 grams
In summary, the correct option is d.: 1.5 grams of glucose is produced from 2.20 g of CO₂.
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What is molarity?
A. A measure of saturation.
B. A ratio of moles of solvent to moles of solution.
C. A measure of moles.
D. A measure of concentration.
Answer:
Molarity is a measure of concentration
I Hope its right if not so advance sorry :)
The molarity measures the number of moles of the solute present per liter of the solution and it measures the concentration of the solution. option D is correct.
What is molarity?Molarity is the amount or the number of moles present in per liter of the solution it is the unit to measure the concentration of the moles.
Unit of molarity will be moles per liter and the temperature does not affect the molarity of the solution. molarity can be calculated by dividing the concentration of the solution by the molar mass of the given element.
molarity = weight / mass × 1000/ volume in liters.
With the help of this formula, we can calculate the molarity.
Therefore, molarity measures the number of moles of the solute present per liter of the solution and it measures the concentration of the solution. option D is correct.
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Write the chemical formula for the following:
a. The conjugate acid of amide ion, NH₂-
b. The conjugate base of nitric acid, HNO₃
Follow the rules of Bronsted Lowry theory
Acids take a HBases donate a HSo
#a
NH_2-
Add a H
Conjugate acid is NH_3#b
HnO_3
Take a H
Conjugate base is NO_3-#1
Conjugate acid means one H+ is added
NH_2+H+=NH_3sw
#2
Conjugate base means donate a H+
HNO_3-H=NO_3-The shape of a molecule is determined by:
A. All of these
B. The number of electron clouds around the atom.
C. The number of bonds.
D. Mutual repulsion between electrons.
QUESTION 11
Identify the reaction type.
KOH + HNO3 -> H2O + KNO3
O combustion
O decomposition
O combination
O single displacement
O double displacement
convert 14.72 kg to ____ mg
Answer:
14720000
Explanation:
1 kg = 1000000 mg
14.72 kg = 14.72 x 1000000
=14720000
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When comparing Be2 and H2:
I. Be2 is more stable because it contains both bonding and antibonding valence electrons.
II. H2 has a higher bond order than Be2.
III. H2 is more stable because it only contains 1s electrons.
IV. H2 is more stable because it is diamagnetic, whereas Be2 is paramagnetic
a. II,III,IV
b.II,III
c.III only
d.I,II
e.III,IV.
Answer:
The answer is "Option b".
Explanation:
H2 does have bond energy of 1, while Be2 has a covalent bond of zero. Be2 has eight electrons, each of which dwells in a distinct orbital. As just a result, four of them are linked molecular orbitals and two are antibonding molecular orbitals, respectively. As just a result, this molecule is unstable. This chemical orbital, with a bond order of 1, has just two electrons. As a result, it is a very solid substance. H2's bond length is higher than Be2's. Since it only has one electron, H2 is more stable than that of other compounds.
The molecular ion is not visible in the mass spectrum of 2-chloro-2- methylpropane. At what m/z value would the molecular ion be if it were visible? What evidence is there in the mass spectrum that suggests that the peak at m/z= 77 contains a chlorine atom?
Answer: hello the complete question is attached below
Visibility of molecular ion = m/z value of 77
Explanation:
For The molecular ion to be visible, it has to be at an m/z value of 77 and this is because molecular ions will have an m/z ratio = molecular mass of given molecule in most cases but not always in all cases.
And the visibility is possible after the removal of CH₃ ion.
ii) Evidence in the mass spectrum that suggests peak at m/z = 77
attached below
