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

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

Step-by-step 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=(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=(P_2V_2)/(RT_2)`..[2]

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

`(n_1)/(n_2)=(1)/(3)`

`n_2=3n_1`

Using above value in [2]

`3n_1=(P_2V_2)/(RT_2)`

`3* (P_1V_1)/(RT_1)=(P_2V_2)/(RT_2)`

Given,
`P_1=P_2,T_1=T_2`

`3* (P_2V_1)/(RT_2)=(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.