Q: Given the reaction $$2\mathrm{H_2$} + 2\mathrm{NO} \rightarrow \mathrm{N_2$} + 2\mathrm{H_2O}$$ with the rate law $$\text{rate} = k[\mathrm{H_2$}]^2[\mathrm{NO}]$$, calculate the rate (in $$\mathrm{M/s}) if$$ $$k = 6.0 \times 10^4$\ \mathrm{M$$^{-2}$$s^{-2}$$}$$, $$[\mathrm{$$H_2$$}] = 0.0010\ \mathrm{M}$$, and $$[\mathrm{NO}] = 0.0020\ \mathrm{M}$.

$$1.2 \times 10$$^{-4}$$\ \mathrm{M/s}$$

Q: Using the following kinetic data for the reaction $$2\mathrm{H_2$} + 2\mathrm{NO} \rightarrow \mathrm{N_2$} + 2\mathrm{H_2O}$$: Exp 1: $$[\mathrm{NO}] = 0.0050\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0025\ \mathrm{M}$$, rate $$= 3.0 \times 10$$^{-3}$$\ \mathrm{M/s}$$ Exp 2: $$[\mathrm{NO}] = 0.0100\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0025\ \mathrm{M}$$, rate $$= 6.0 \times 10$$^{-3}$$\ \mathrm{M/s}$$ Exp 3: $$[\mathrm{NO}] = 0.0050\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0050\ \mathrm{M}$$, rate $$= 6.0 \times 10$$^{-3}$$\ \mathrm{M/s}$$ Exp 4: $$[\mathrm{NO}] = 0.0100\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0050\ \mathrm{M}$$, rate $$= 1.2 \times 10$$^{-2}$$\ \mathrm{M/s}$$ What is the correct rate law for this reaction?

$$\text{rate} = k[\mathrm{NO}][\mathrm{H_2$}]$$

Q: A reaction has an activation energy ($$E_a) of$$ $$56.8\ \mathrm{kJ/mol}$$ and a frequency factor ($$A) of$$ $$1.5 \times 10$$^{11}$$\ \mathrm{s$$^{-1}$$}. $$Calculate the rate constant ($$k) at$$ $$25^\circ\mathrm{C}$$ using the Arrhenius equation. ($$R = 8.314\ \mathrm{J/(mol\cdot K)})$$

$$k = 1.5 \times 10$$^{11}$$ \exp\left(-\dfrac{56800}{8.314 \times 298}\right)$$

Q: A solution is prepared by dissolving a nonvolatile solute in water. Which equation correctly predicts the vapor pressure of the solution?

$$P_{\text{soln}} = X_{\text{solvent}} P_{\text{solvent}}^\circ$$

Q: A patient receives a saline solution intravenously. If the molality ($$m) of $$the solution is $$0.15\ \mathrm{mol/kg}$$ and the van't Hoff factor ($$i) is$$ $$2$$, what is the expected freezing point depression ($$\Delta T_f) if$$ $$K_f$$ for water is $$1.86\ \mathrm{\degree C\cdot kg/mol}$$?

$$\Delta T_f = i K_f m = 2 \times 1.86 \times 0.15 = 0.558\ \degree \mathrm{C}$$

Q: A gas occupies $$5.0\ \mathrm{L} at$$ $$2.0\ \mathrm{atm}$$ and $$300\ \mathrm{K}. $$How many moles of gas are present? ($$R = 0.0821\ \mathrm{L\cdot atm/(mol\cdot K)})$$

$$n = \dfrac{PV}{RT} = \dfrac{2.0 \times 5.0}{0.0821 \times 300} = 0.41\ \mathrm{mol}$$

Question 1

For the reaction $$\mathrm{N_2$ + 3H_2 \rightarrow 2NH_3}$$, if the average rate of consumption of $$\mathrm{H_2$} is$$ $$0.0277\ \mathrm{M/s}$$, what is the average rate of production of $$\mathrm{NH_3$}$$?

Accepted Answer

$$0.0185\ \mathrm{M/s}$$

Question 2

Given the reaction $$2\mathrm{H_2$} + 2\mathrm{NO} ightarrow \mathrm{N_2$} + 2\mathrm{H_2O}$$ with the rate law $$	ext{rate} = k[\mathrm{H_2$}]^2[\mathrm{NO}]$$, calculate the rate (in $$\mathrm{M/s}) if$$ $$k = 6.0 	imes 10^4$\ \mathrm{M$$^{-2}$$s^{-2}$$}$$, $$[\mathrm{$$H_2$$}] = 0.0010\ \mathrm{M}$$, and $$[\mathrm{NO}] = 0.0020\ \mathrm{M}$.

Accepted Answer

$$1.2 	imes 10$$^{-4}$$\ \mathrm{M/s}$$

Question 3

Using the following kinetic data for the reaction $$2\mathrm{H_2$} + 2\mathrm{NO} ightarrow \mathrm{N_2$} + 2\mathrm{H_2O}$$:

Exp 1: $$[\mathrm{NO}] = 0.0050\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0025\ \mathrm{M}$$, rate $$= 3.0 	imes 10$$^{-3}$$\ \mathrm{M/s}$$
Exp 2: $$[\mathrm{NO}] = 0.0100\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0025\ \mathrm{M}$$, rate $$= 6.0 	imes 10$$^{-3}$$\ \mathrm{M/s}$$
Exp 3: $$[\mathrm{NO}] = 0.0050\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0050\ \mathrm{M}$$, rate $$= 6.0 	imes 10$$^{-3}$$\ \mathrm{M/s}$$
Exp 4: $$[\mathrm{NO}] = 0.0100\ \mathrm{M}$$, $$[\mathrm{H_2$}] = 0.0050\ \mathrm{M}$$, rate $$= 1.2 	imes 10$$^{-2}$$\ \mathrm{M/s}$$

What is the correct rate law for this reaction?

Accepted Answer

$$	ext{rate} = k[\mathrm{NO}][\mathrm{H_2$}]$$

Question 4

What is the half-life ($$t_{1/2}) of a $$first-order reaction with a rate constant $$k = 0.693\ \mathrm{s$$^{-1}$$}$$?

Accepted Answer

$$t_{1/2} = \dfrac{0.693}{0.693} = 1\ \mathrm{s}$$

Question 5

A reaction has an activation energy ($$E_a) of$$ $$56.8\ \mathrm{kJ/mol}$$ and a frequency factor ($$A) of$$ $$1.5 	imes 10$$^{11}$$\ \mathrm{s$$^{-1}$$}. $$Calculate the rate constant ($$k) at$$ $$25^\circ\mathrm{C}$$ using the Arrhenius equation. ($$R = 8.314\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$k = 1.5 	imes 10$$^{11}$$ \exp\left(-\dfrac{56800}{8.314 	imes 298}ight)$$

Question 6

For a reaction, the rate constant $$k is$$ $$3.20 	imes 10$$^{-5}$$\ \mathrm{s$$^{-1}$$} at$$ $$450\ \mathrm{K}$$ and $$9.40 	imes 10$$^{-3}$$\ \mathrm{s$$^{-1}$$} at$$ $$500\ \mathrm{K}. $$What is the activation energy ($$E_a) $$for this reaction? Use the two-point Arrhenius equation.

Accepted Answer

$$E_a = -R \dfrac{\ln\left(\dfrac{k_2$}{k_1$}\right)}{\dfrac{1}{T_2$} - \dfrac{1}{T_1$}}$$

Question 7

Which of the following best describes the relationship between $$K_p$$ and $$K_c$$ for a gaseous reaction?

Accepted Answer

$$K_p = K_c \cdot (RT$$)^{\Delta n}$$

Question 8

A solution is prepared by dissolving a nonvolatile solute in water. Which equation correctly predicts the vapor pressure of the solution?

Accepted Answer

$$P_{	ext{soln}} = X_{	ext{solvent}} P_{	ext{solvent}}^\circ$$

Question 9

A patient receives a saline solution intravenously. If the molality ($$m) of $$the solution is $$0.15\ \mathrm{mol/kg}$$ and the van't Hoff factor ($$i) is$$ $$2$$, what is the expected freezing point depression ($$\Delta T_f) if$$ $$K_f$$ for water is $$1.86\ \mathrm{\degree C\cdot kg/mol}$$?

Accepted Answer

$$\Delta T_f = i K_f m = 2 	imes 1.86 	imes 0.15 = 0.558\ \degree \mathrm{C}$$

Question 10

A gas occupies $$5.0\ \mathrm{L} at$$ $$2.0\ \mathrm{atm}$$ and $$300\ \mathrm{K}. $$How many moles of gas are present? ($$R = 0.0821\ \mathrm{L\cdot atm/(mol\cdot K)})$$

Accepted Answer

$$n = \dfrac{PV}{RT} = \dfrac{2.0 	imes 5.0}{0.0821 	imes 300} = 0.41\ \mathrm{mol}$$

Question 11

Which equation correctly relates osmotic pressure ($$\pi) to $$molarity ($$M$$), temperature ($$T$$), and the gas constant ($$R$$)?

Accepted Answer

$$\pi = MRT$$

Question 12

A sample of gas at STP occupies $$44.8\ \mathrm{L}. $$How many moles of gas are present?

Accepted Answer

$$n = \dfrac{44.8}{22.4} = 2.0\ \mathrm{mol}$$

Question 13

A reaction has a rate constant $$k$$ that doubles when the temperature increases from $$300\ \mathrm{K} to$$ $$310\ \mathrm{K}. $$What is the approximate activation energy ($$E_a) in$$ $$\mathrm{J/mol}$$? Use the one-point Arrhenius equation.

Accepted Answer

$$E_a = R \dfrac{\ln(2)}{\dfrac{1}{300} - \dfrac{1}{310}}$$

Question 14

Which of the following is the correct conversion for $$1\ \mathrm{atm} to$$ $$\mathrm{Pa}$$?

Accepted Answer

$$1\ \mathrm{atm} = 101,325\ \mathrm{Pa}$$

Question 15

A chemist needs to calculate the boiling point elevation ($$\Delta T_b) $$for a solution. Which equation should be used?

Accepted Answer

$$\Delta T_b = i K_b m$$

Question 16

Which formula correctly converts Celsius to Kelvin?

Accepted Answer

$$K = ^\circ\mathrm{C} + 273$$

Question 17

A reaction has a rate law $$	ext{rate} = k[\mathrm{A}]^2[\mathrm{B}]. If$$ $$[\mathrm{A}] is $$doubled and $$[\mathrm{B}] is $$tripled, by what factor does the rate increase?

Accepted Answer

The rate increases by a factor of $$2^2$$ 	imes 3 = 12$$

Question 18

Which of the following is the correct value for Avogadro’s number?

Accepted Answer

$$6.02 	imes 10$$^{23}$$

General Chemistry: Reaction Rates, Rate Laws, and Arrhenius Equation Guidance

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