Question

reaction stoichiometry involving gases
consider the chemical reaction:
c(s) + h₂o(g) → co(g) + h₂(g)
how many litres of hydrogen gas are formed from the complete reaction of 15.7 g c? assume that the hydrogen gas is collected at a pressure of 1.0 bar and a temperature of 355 k.

Explanation:

Step1: Calculate the moles of \(C\)

The molar mass of \(C\) is \(M = 12.01\space g/mol\).
The number of moles of \(C\), \(n_{C}=\frac{m}{M}=\frac{15.7\space g}{12.01\space g/mol}\approx1.307\space mol\)

Step2: Determine the moles of \(H_{2}\) using stoichiometry

From the balanced equation \(C(s)+H_{2}O(g)\to CO(g) + H_{2}(g)\), the mole ratio of \(C\) to \(H_{2}\) is \(1:1\). So \(n_{H_{2}}=n_{C} = 1.307\space mol\)

Step3: Use the ideal gas law \(PV = nRT\) to find the volume of \(H_{2}\)

We know that \(P = 1.0\space bar\), \(n=1.307\space mol\), \(T = 355\space K\), and \(R=0.0831\space L\cdot bar/mol\cdot K\)
Rearrange the ideal gas law for \(V\): \(V=\frac{nRT}{P}\)
Substitute the values: \(V=\frac{1.307\space mol\times0.0831\space L\cdot bar/mol\cdot K\times355\space K}{1.0\space bar}\)
\(V=\frac{1.307\times0.0831\times355}{1}\space L\)
\(1.307\times0.0831 = 0.1086\)
\(0.1086\times355=38.5\space L\)

Answer:

\(38.5\space L\)