Q1. For the reaction N2 + 3 H2 → 2 NH3, the average rate of consumption of H2 is 0.0277 M/s. What is the average rate of change (M/s) for production of NH3?

Background

Topic: Reaction Rates and Stoichiometry

This question tests your understanding of how reaction rates relate to stoichiometry. Specifically, it asks you to relate the rate of consumption of a reactant to the rate of formation of a product using the balanced chemical equation.

Key Terms and Formulas

• Average rate: Change in concentration of a species per unit time.

• Stoichiometry: The coefficients in the balanced equation relate the rates of consumption and formation of reactants and products.

General formula for relating rates:

$-\frac{1}{a}\frac{d[\text{A}]}{dt} = -\frac{1}{b}\frac{d[\text{B}]}{dt} = \frac{1}{c}\frac{d[\text{C}]}{dt}$

For this reaction: $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$

Step-by-Step Guidance

1. Write the rate expressions for each species using the stoichiometric coefficients: $-\frac{d[\text{N}_2]}{dt} = -\frac{1}{3}\frac{d[\text{H}_2]}{dt} = \frac{1}{2}\frac{d[\text{NH}_3]}{dt}$

2. Identify the given rate: The rate of consumption of H2 is $0.0277$ M/s, so $-\frac{d[\text{H}_2]}{dt} = 0.0277$ M/s.

3. Set up the relationship between the rate of H2 consumption and NH3 production using the stoichiometry: $-\frac{1}{3}\frac{d[\text{H}_2]}{dt} = \frac{1}{2}\frac{d[\text{NH}_3]}{dt}$

4. Rearrange to solve for $\frac{d[\text{NH}_3]}{dt}$ in terms of $\frac{d[\text{H}_2]}{dt}$.

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Q2. The reaction 2 H2 + 2 NO2 → N2 + 2 H2O has the rate law: rate = k[H2]2[NO]. What is the rate of the reaction (M/s) if the rate constant k is 6.0 x 104 (M−2/s), [H2] = 0.0010 M, and [NO] = 0.0020 M?

Background

Topic: Rate Laws and Calculating Reaction Rates

This question tests your ability to use a given rate law to calculate the reaction rate when provided with the rate constant and reactant concentrations.

Key Terms and Formulas

• Rate law: An equation that relates the reaction rate to the concentrations of reactants and the rate constant.

• Rate constant (k): A proportionality constant specific to a reaction at a given temperature.

Given rate law: $\text{rate} = k[\text{H}_2]^2[\text{NO}]$

Step-by-Step Guidance

1. Identify the values given:

   • $k = 6.0 \times 10^4$ M−2/s

   • $[\text{H}_2] = 0.0010$ M

   • $[\text{NO}] = 0.0020$ M

2. Write the rate law with the given values: $\text{rate} = k[\text{H}_2]^2[\text{NO}]$

3. Substitute the values into the equation: $\text{rate} = (6.0 \times 10^4) \times (0.0010)^2 \times (0.0020)$

4. Calculate $(0.0010)^2$ and then multiply by $0.0020$ and $k$ (but stop before the final multiplication).

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Q3. Determining the rate law from kinetic data:

Background

Topic: Determining Rate Laws from Experimental Data

This question tests your ability to analyze how changes in reactant concentrations affect the reaction rate, allowing you to deduce the order of reaction with respect to each reactant.

Key Terms and Formulas

• Rate law: $\text{rate} = k[\text{NO}]^m[\text{H}_2]^n$

• Order of reaction: The exponent of each reactant in the rate law.

Step-by-Step Guidance

1. Compare experiments where only one reactant concentration changes to determine the order with respect to that reactant.

   • For example, compare Exp 1 and Exp 2 to find the order with respect to [NO].

   • Compare Exp 1 and Exp 3 to find the order with respect to [H2].

2. Set up the ratio of rates for the two experiments, keeping the other reactant constant.

3. Express the ratio in terms of the unknown order (exponent) and solve for it (but stop before the final calculation).

4. Repeat for the other reactant to find both orders.

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Q4. What is the half-life of a first-order reaction if the rate constant k is given?

Background

Topic: First-Order Kinetics and Half-Life

This question tests your understanding of the relationship between the rate constant and the half-life for a first-order reaction.

Key Terms and Formulas

• Half-life ($t_{1/2}$): The time required for the concentration of a reactant to decrease by half.

• First-order reaction: A reaction whose rate depends linearly on the concentration of one reactant.

Formula for half-life of a first-order reaction:

$t_{1/2} = \frac{0.693}{k}$

Step-by-Step Guidance

1. Identify the value of the rate constant $k$ (it should be given in the problem).

2. Write the formula for the half-life of a first-order reaction: $t_{1/2} = \frac{0.693}{k}$

3. Substitute the value of $k$ into the formula (but do not calculate the final value).

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Q5. The activation energy of a reaction is 56.8 kJ/mol and the frequency factor is 1.5 x 1011/s. Calculate the rate constant of the reaction at 25°C using the one-point Arrhenius equation.

Background

Topic: Arrhenius Equation and Temperature Dependence of Rate Constants

This question tests your ability to use the Arrhenius equation to calculate the rate constant at a given temperature, given the activation energy and frequency factor.

Key Terms and Formulas

• Arrhenius equation: $k = Ae^{-E_a/(RT)}$

• $A$: Frequency factor (pre-exponential factor)

• $E_a$: Activation energy (in J/mol)

• $R$: Gas constant ($8.314$ J/(mol·K))

• $T$: Temperature in Kelvin

Step-by-Step Guidance

1. Convert the activation energy from kJ/mol to J/mol (multiply by 1000).

2. Convert the temperature from °C to K by adding 273.

3. Write the Arrhenius equation: $k = Ae^{-E_a/(RT)}$

4. Substitute the values for $A$, $E_a$, $R$, and $T$ into the equation (but do not calculate the final value).

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Q6. A reaction has a rate constant k of 3.20 x 10−5/s at 450 K and a rate constant k of 9.40 x 10−3/s at 500 K. What is the activation energy Ea for this reaction? (Use the two-point Arrhenius equation.)

Background

Topic: Arrhenius Equation and Activation Energy

This question tests your ability to use the two-point Arrhenius equation to determine the activation energy from rate constants at two different temperatures.

Key Terms and Formulas

• Two-point Arrhenius equation: $\ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

• $k_1$, $k_2$: Rate constants at temperatures $T_1$ and $T_2$

• $E_a$: Activation energy

• $R$: Gas constant ($8.314$ J/(mol·K))

Step-by-Step Guidance

1. Identify the values:

   • $k_1 = 3.20 \times 10^{-5}$/s at $T_1 = 450$ K

   • $k_2 = 9.40 \times 10^{-3}$/s at $T_2 = 500$ K

2. Write the two-point Arrhenius equation: $\ln\left(\frac{k_2}{k_1}\right) = -\frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

3. Calculate $\ln\left(\frac{k_2}{k_1}\right)$ (but do not compute the final value).

4. Calculate $\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$ (but do not compute the final value).

5. Rearrange the equation to solve for $E_a$ (but do not calculate the final value).

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