Question

given the following balanced equation, determine the rate of reaction with respect to nh3.
n2(g) + 3h2(g) → 2nh3(g)
a) rate = -\frac{1}{2}\frac{\deltanh3}{\delta t}
d) rate = +\frac{2\deltanh3}{\delta t}
b) rate = -\frac{\deltanh3}{\delta t}
e) rate = +\frac{\deltanh3}{\delta t}
c) rate = +\frac{1}{2}\frac{\deltanh3}{\delta t}

Explanation:

Step1: Recall the general rate expression

For a reaction \(aA + bB
ightarrow cC + dD\), the rate is given by \(\text{Rate}=-\frac{1}{a}\frac{\Delta[A]}{\Delta t}=-\frac{1}{b}\frac{\Delta[B]}{\Delta t}=\frac{1}{c}\frac{\Delta[C]}{\Delta t}=\frac{1}{d}\frac{\Delta[D]}{\Delta t}\)

Step2: Identify coefficients for the given reaction

In the reaction \(N_2(g)+3H_2(g)
ightarrow 2NH_3(g)\), \(a = 1\) (for \(N_2\)), \(b = 3\) (for \(H_2\)), \(c = 2\) (for \(NH_3\))

Step3: Write the rate with respect to \(NH_3\)

Using the formula \(\text{Rate}=\frac{1}{c}\frac{\Delta[C]}{\Delta t}\), substituting \(c = 2\) and \(C=NH_3\), we get \(\text{Rate}=\frac{1}{2}\frac{\Delta[NH_3]}{\Delta t}\)

Answer:

C. Rate \(=+\frac{1}{2}\frac{\Delta[NH3]}{\Delta t}\)