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Question: For a zero order chemical reaction, $2NH_3(g) \rightarrow N_2(g) + 3H_2(g)$ rate of reaction = 0.1...

For a zero order chemical reaction,

2NH3(g)→N2(g)+3H2(g)2NH_3(g) \rightarrow N_2(g) + 3H_2(g)

rate of reaction = 0.1 atm/sec. Initially only NH3NH_3 is present & Its pressure = 3 atm

Rate of disappearance of NH3NH_3 will be (in atm/sec)

Answer

0.2

Explanation

Solution

The rate of a chemical reaction is related to the rate of disappearance of reactants and the rate of appearance of products by their stoichiometric coefficients. For the given reaction: 2NH3(g)→N2(g)+3H2(g)2NH_3(g) \rightarrow N_2(g) + 3H_2(g)

The general expression for the rate of reaction is: Rate =−12d[NH3]dt=+11d[N2]dt=+13d[H2]dt= -\frac{1}{2}\frac{d[NH_3]}{dt} = +\frac{1}{1}\frac{d[N_2]}{dt} = +\frac{1}{3}\frac{d[H_2]}{dt}

We are given the rate of reaction = 0.1 atm/sec. We need to find the rate of disappearance of NH3NH_3, which is −d[NH3]dt-\frac{d[NH_3]}{dt}.

From the rate expression, we can equate the overall rate of reaction to the term involving NH3NH_3: Rate =−12d[NH3]dt= -\frac{1}{2}\frac{d[NH_3]}{dt}

Substitute the given value for the rate of reaction: 0.1 atm/sec=−12d[NH3]dt0.1 \text{ atm/sec} = -\frac{1}{2}\frac{d[NH_3]}{dt}

Now, solve for −d[NH3]dt-\frac{d[NH_3]}{dt}: −d[NH3]dt=2×0.1 atm/sec-\frac{d[NH_3]}{dt} = 2 \times 0.1 \text{ atm/sec} −d[NH3]dt=0.2 atm/sec-\frac{d[NH_3]}{dt} = 0.2 \text{ atm/sec}

The information about the reaction being zero order and the initial pressure of NH3NH_3 (3 atm) is not required for this calculation, as the overall rate of reaction is directly provided. For a zero-order reaction, the rate is constant and independent of reactant concentrations, but here the constant rate itself is given.