Question

Methanol, ‍ , can be produced in industrial plants by reacting carbon dioxide with hydrogen in the presence of a catalyst. Water is the other product. How many volumes of hydrogen are required for each volume of carbon dioxide when each gas is at the same temperature and pressure?

Answer 1

Answer:

Volume of hydrogen gas required for each volume of carbon dioxide is 3 times the volume of  carbon dioxide gas.

Explanation:

$CO_2+3H_2\rightarrow CH_3OH+H_2O$

Volume of the carbon dioxide gas = $V_1$

Temperature of the carbon dioxide gas = $T_1$

Pressure of the carbon dioxide gas = $P_1$

Moles of carbon dioxide gas = $n_1$

$P_1V_1=n_1RT_1$ (ideal gas equation )

$n_1=\frac{P_1V_1}{RT_1}$..[1]

Volume of the hydrogen  gas = $V_2$

Temperature of the hydrogen   gas = $T_2$

Pressure of the hydrogen   gas = $P_2$

Moles of hydrogen  gas = $n_2$

$n_2=\frac{P_2V_2}{RT_2}$..[2]

According to reaction 1 mole of carbon dioxide reacts with 3 moles of hydrogen gas.

$\frac{n_1}{n_2}=\frac{1}{3}$

$n_2=3n_1$

Using above value in [2]

$3n_1=\frac{P_2V_2}{RT_2}$

$3\times \frac{P_1V_1}{RT_1}=\frac{P_2V_2}{RT_2}$

Given, $P_1=P_2,T_1=T_2$

$3\times \frac{P_2V_1}{RT_2}=\frac{P_2V_2}{RT_2}$

$3V_1=V_2$

Volume of hydrogen gas = 3 × volume of carbon dioxide gas

Volume of hydrogen gas required for each volume of carbon dioxide is 3 times the volume of carbon dioxide gas.