16) A scientist conducts an experiment to determine the rate of the following reaction: \[ \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g}) \] If the initial concentration of \( \mathrm{H}_{2} \) was 0.150 M and the concentration of \( \mathrm{H}_{2} \) was 0.050 M after 2.10 s , what is the average rate of the reaction? A. \( 0.048 \mathrm{M} / \mathrm{s} \) B. \( 0.016 \mathrm{M} / \mathrm{s} \) C. \( 0.072 \mathrm{M} / \mathrm{s} \) (1). \( 0.032 \mathrm{M} / \mathrm{s} \) \[ \begin{array}{l} \frac{1}{0.050}=\frac{1}{0.150}+2.10 t \\ \frac{40}{3}=2.102 \end{array} \]

To find the average rate of the reaction, we can use the change in concentration of the reactant \( \mathrm{H}_{2} \) over the time interval. The average rate of a reaction can be expressed as: \[ \text{Average Rate} = -\frac{\Delta [\mathrm{H}_{2}]}{\Delta t} \] Where: - \( \Delta [\mathrm{H}_{2}] \) is the change in concentration of \( \mathrm{H}_{2} \) - \( \Delta t \) is the change in time ### Step 1: Calculate the change in concentration of \( \mathrm{H}_{2} \) The initial concentration of \( \mathrm{H}_{2} \) is given as \( 0.150 \, \mathrm{M} \) and the concentration after \( 2.10 \, \mathrm{s} \) is \( 0.050 \, \mathrm{M} \). \[ \Delta [\mathrm{H}_{2}] = [\mathrm{H}_{2}]_{\text{initial}} - [\mathrm{H}_{2}]_{\text{final}} = 0.150 \, \mathrm{M} - 0.050 \, \mathrm{M} = 0.100 \, \mathrm{M} \] ### Step 2: Calculate the change in time The time interval \( \Delta t \) is given as \( 2.10 \, \mathrm{s} \). ### Step 3: Calculate the average rate Now we can substitute the values into the average rate formula: \[ \text{Average Rate} = -\frac{0.100 \, \mathrm{M}}{2.10 \, \mathrm{s}} = -0.047619 \, \mathrm{M/s} \] Since we are interested in the rate (which is a positive value), we take the absolute value: \[ \text{Average Rate} \approx 0.048 \, \mathrm{M/s} \] ### Conclusion The average rate of the reaction is approximately \( 0.048 \, \mathrm{M/s} \). Therefore, the correct answer is: **A. \( 0.048 \, \mathrm{M/s} \)**.