Question

ch₄ + 2 o₂ → co₂ + 2 h₂o

1. if 0.51 moles of o₂ are used, how many moles of ch₄ are also used?
2. if 0.45 moles of h₂o are produced, how many moles of co₂ are also produced?

Explanation:

Step1: Determine mole ratio from reaction equation

From the balanced equation \(CH_4 + 2O_2
ightarrow CO_2 + 2H_2O\), the mole ratio of \(CH_4\) to \(O_2\) is \(1:2\), and the mole ratio of \(CO_2\) to \(H_2O\) is \(1:2\).

Step2: Calculate moles of \(CH_4\)

Let \(n(CH_4)\) be the moles of \(CH_4\). Using the ratio \(\frac{n(CH_4)}{n(O_2)}=\frac{1}{2}\), with \(n(O_2) = 0.51\) mol. Then \(n(CH_4)=\frac{1}{2}\times n(O_2)=\frac{1}{2}\times0.51 = 0.255\) mol.

Step3: Calculate moles of \(CO_2\)

Let \(n(CO_2)\) be the moles of \(CO_2\). Using the ratio \(\frac{n(CO_2)}{n(H_2O)}=\frac{1}{2}\), with \(n(H_2O)=0.45\) mol. Then \(n(CO_2)=\frac{1}{2}\times n(H_2O)=\frac{1}{2}\times0.45 = 0.225\) mol.

Answer:

For the first question (moles of \(CH_4\)): \(0.255\) mol.
For the second question (moles of \(CO_2\)): \(0.225\) mol.