Question

Consider the combustion of ethane: $$ 2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ If the ethane is burning at the rate of \(0.20 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s},\) at what rates are \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) being produced?

Short answer

Answer: The rate of CO2 production is 0.10 mol/L·s, and the rate of H2O production is 0.067 mol/L·s.

Step-by-step solution

Analyze the balanced chemical equation

We are given a chemical equation representing the combustion of ethane: $$ 2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ Now, we need to find the relationship between the combustion of ethane and the formation of CO2 and H2O. For this, we will use stoichiometry.

Determine the stoichiometric coefficients

From the balanced equation, we can see that: 1. When 2 moles of ethane burn, 4 moles of CO2 are produced. 2. When 2 moles of ethane burn, 6 moles of H2O are produced. 3. The rate of consumption of ethane is given as 0.20 mol/L·s

Find the rate of CO2 production

To find the rate of CO2 production, we can use the stoichiometric coefficients and the given rate of combustion of ethane. Since the ratio of ethane to CO2 is 2:4 or 1:2, we can find the rate of CO2 production as follows: $$ \text{Rate of CO2 production} = \frac{1}{2}\times\text{Rate of ethane combustion} $$ $$ \text{Rate of CO2 production} = \frac{1}{2}\times0.20\ \mathrm{mol/L\cdot s} $$ $$ \text{Rate of CO2 production} = 0.10\ \mathrm{mol/L\cdot s} $$

Find the rate of H2O production

To find the rate of H2O production, we can use the stoichiometric coefficients and the given rate of combustion of ethane. Since the ratio of ethane to H2O is 2:6 or 1:3, we can find the rate of H2O production as follows: $$ \text{Rate of H2O production} = \frac{1}{3}\times\text{Rate of ethane combustion} $$ $$ \text{Rate of H2O production} = \frac{1}{3}\times0.20\ \mathrm{mol/L\cdot s} $$ $$ \text{Rate of H2O production} = 0.067\ \mathrm{mol/L\cdot s} $$ Finally, we have derived the rate of production for both CO2 and H2O. The rate of CO2 production is 0.10 mol/L·s, and the rate of H2O production is 0.067 mol/L·s.