Correct answer Carries: 4.
Wrong Answer Carries: -1.
A zero-order reaction has an initial concentration of \( 0.15 \, \text{mol L}^{-1} \) and a rate constant of \( 2.5 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \). What is the half-life?
For zero-order, \( t_{1/2} = \frac{[\text{R}]_0}{2k} \).
Given: \( [\text{R}]_0 = 0.15 \, \text{mol L}^{-1} \), \( k = 2.5 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \).
\( t_{1/2} = \frac{0.15}{2 \times 2.5 \times 10^{-3}} = \frac{0.15}{5.0 \times 10^{-3}} = 30 \, \text{s} \).
The half-life of a first-order reaction is 20 minutes. What is the rate constant?
For a first-order reaction, \( t_{1/2} = \frac{0.693}{k} \).
Given: \( t_{1/2} = 20 \, \text{min} \).
\( k = \frac{0.693}{20} = 0.03465 \, \text{min}^{-1} \approx 3.465 \times 10^{-2} \, \text{min}^{-1} \).
A reaction has a rate constant of \( 0.05 \, \text{L mol}^{-1} \text{s}^{-1} \). What is its order?
For a second-order reaction, the unit of \( k \) is \( \text{L mol}^{-1} \text{s}^{-1} \).
Given: \( k = 0.05 \, \text{L mol}^{-1} \text{s}^{-1} \), which matches the unit for a second-order reaction.
Thus, the order is 2.
A first-order reaction has a rate constant of \( 0.0115 \, \text{min}^{-1} \). What percentage of the reactant remains after 60 minutes?
\( \log \frac{[\text{R}]_0}{[\text{R}]} = \frac{k t}{2.303} \).
\( \log \frac{[\text{R}]_0}{[\text{R}]} = \frac{0.0115 \times 60}{2.303} \approx 0.301 \), \( \frac{[\text{R}]_0}{[\text{R}]} = 10^{0.301} \approx 2 \).
Fraction remaining = \( \frac{1}{2} = 0.5 \), percentage = \( 50\% \).
A reaction’s rate increases by 2.25 times when the concentration of the reactant is increased by 1.5 times. What is the order of the reaction?
Rate = \( k [\text{A}]^n \). New rate: \( k (1.5[\text{A}])^n = 2.25 k [\text{A}]^n \), so \( 1.5^n = 2.25 \).
\( n \log 1.5 = \log 2.25 \), \( n \times 0.176 = 0.352 \), \( n \approx 2 \).
A reaction has the rate law \( \text{Rate} = k[\text{A}]^2[\text{B}] \). If the concentration of A is tripled and B is doubled, by how many times will the rate increase?
Initial rate = \( k [\text{A}]^2 [\text{B}] \).
New rate = \( k (3[\text{A}])^2 (2[\text{B}]) = k \times 9 [\text{A}]^2 \times 2 [\text{B}] = 18 k [\text{A}]^2 [\text{B}] \).
Rate increases by 18 times.
A second-order reaction has a rate constant of \( 0.02 \, \text{L mol}^{-1} \text{s}^{-1} \) and an initial concentration of \( 0.2 \, \text{mol L}^{-1} \). What is the half-life?
For second-order, \( t_{1/2} = \frac{1}{k [\text{A}]_0} \).
Given: \( k = 0.02 \, \text{L mol}^{-1} \text{s}^{-1} \), \( [\text{A}]_0 = 0.2 \, \text{mol L}^{-1} \).
\( t_{1/2} = \frac{1}{0.02 \times 0.2} = \frac{1}{0.004} = 250 \, \text{s} \).
A first-order reaction is 20% complete in 10 minutes. What is the rate constant?
For first-order, \( k = \frac{2.303}{t} \log \frac{[\text{R}]_0}{[\text{R}]} \).
20% complete means 80% remains, \( \frac{[\text{R}]}{[\text{R}]_0} = 0.8 \), \( \frac{[\text{R}]_0}{[\text{R}]} = 1.25 \).
\( k = \frac{2.303}{10} \log 1.25 = \frac{2.303 \times 0.0969}{10} \approx 0.0223 \, \text{min}^{-1} \).
For a reaction \( \text{A} + 2\text{B} \to \text{C} \), the rate of disappearance of B is \( 0.06 \, \text{mol L}^{-1} \text{s}^{-1} \). What is the rate of reaction?
Rate of reaction = \( -\frac{1}{2} \frac{\Delta[\text{B}]}{\Delta t} \).
Given: \( -\frac{\Delta[\text{B}]}{\Delta t} = 0.06 \, \text{mol L}^{-1} \text{s}^{-1} \).
Rate = \( \frac{0.06}{2} = 0.03 \, \text{mol L}^{-1} \text{s}^{-1} \).
A reaction has the rate law \( \text{Rate} = k[\text{A}]^2 \). If the concentration of A is increased by 5 times, by how many times will the rate increase?
Initial rate = \( k [\text{A}]^2 \).
New rate = \( k (5[\text{A}])^2 = k \times 25 [\text{A}]^2 = 25 \times \text{initial rate} \).
Rate increases by 25 times.
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