Question

Ammonia is produced by the reaction between nitrogen and hydrogen gases. (a) Write a balanced equation using smallest wholenumber coefficients for the reaction. (b) Write an expression for the rate of reaction in terms of \(\Delta\left[\mathrm{NH}_{3}\right]\) (c) The concentration of ammonia increases from \(0.257 \mathrm{M}\) to \(0.815 \mathrm{M}\) in \(15.0 \mathrm{~min} .\) Calculate the average rate of reaction over this time interval.

Short answer

Question: Write the balanced equation for the reaction between nitrogen gas and hydrogen gas to produce ammonia gas, and calculate the average rate of reaction if the concentration of ammonia increases from 0.257 M to 0.815 M in 15.0 minutes. Answer: The balanced equation for the reaction is \(\ce{N2 + 3H2 -> 2NH3}\). The average rate of reaction for this time interval is \(0.00031\, \mathrm{M/s}\).

Step-by-step solution

a) Writing the balanced equation for the reaction.

To write a balanced equation, first, list the reactants and products and their correct formulas. Nitrogen gas (N2) and hydrogen gas (H2) are the reactants, and ammonia gas (NH3) is the product. Now, balance the equation by adjusting the coefficients. The balanced equation is: \[ \ce{N2 + 3H2 -> 2NH3} \]

b) Writing an expression for the rate of reaction.

To write an expression for the rate of reaction in terms of the change in ammonia concentration (\(\Delta \left[\mathrm{NH_{3}}\right]\)), we need to know the stoichiometry of the reaction. From the balanced equation, we can see that 2 moles of ammonia are produced when 1 mole of nitrogen and 3 moles of hydrogen react. So, the rate of reaction is equal to half the rate of change in concentration of ammonia. Mathematically, this can be expressed as: \[ \text{Rate of Reaction} = \frac{1}{2} \times \frac{\Delta \left[\mathrm{NH_{3}}\right]}{\Delta t} \]

c) Calculating the average rate of reaction.

To calculate the average rate of reaction, we will use the provided information that the concentration of ammonia increases from \(0.257\,\mathrm{M}\) to \(0.815\,\mathrm{M}\) in \(15.0\,\mathrm{min}\). First, find the change in concentration of ammonia, \(\Delta \left[\mathrm{NH_{3}}\right]\) using the final and initial concentrations: \[ \Delta \left[\mathrm{NH}_{3}\right]=\left[\mathrm{NH}_{3}\right]_{\text{final}}-\left[\mathrm{NH}_{3}\right]_{\text{initial}}=0.815\,\mathrm{M}-0.257\,\mathrm{M} = 0.558 \,\mathrm{M} \] Now, we will find the change in time, \(\Delta t\), in seconds: \[ \Delta t = 15.0\, \mathrm{min} \times \frac{60\, \mathrm{s}}{1\, \mathrm{min}} = 900\, \mathrm{s} \] Finally, we will use the expression we derived in part (b) to calculate the average rate of reaction: \[ \text{Average Rate of Reaction} = \frac{1}{2} \times \frac{0.558 \, \mathrm{M}}{900\, \mathrm{s}} = 0.00031\, \mathrm{M/s} \] Therefore, the average rate of reaction over this time interval is \(0.00031\, \mathrm{M/s}\).