Respuesta :
Answer:
Volume of hydrogen gas required for each volume of carbon dioxide is 3 times the volume of carbon dioxide gas.
Explanation:
[tex]CO_2+3H_2\rightarrow CH_3OH+H_2O[/tex]
Volume of the carbon dioxide gas = [tex]V_1[/tex]
Temperature of the carbon dioxide gas = [tex]T_1[/tex]
Pressure of the carbon dioxide gas = [tex]P_1[/tex]
Moles of carbon dioxide gas = [tex]n_1[/tex]
[tex]P_1V_1=n_1RT_1[/tex] (ideal gas equation )
[tex]n_1=\frac{P_1V_1}{RT_1}[/tex]..[1]
Volume of the hydrogen gas = [tex]V_2[/tex]
Temperature of the hydrogen gas = [tex]T_2[/tex]
Pressure of the hydrogen gas = [tex]P_2[/tex]
Moles of hydrogen gas = [tex]n_2[/tex]
[tex]n_2=\frac{P_2V_2}{RT_2}[/tex]..[2]
According to reaction 1 mole of carbon dioxide reacts with 3 moles of hydrogen gas.
[tex]\frac{n_1}{n_2}=\frac{1}{3}[/tex]
[tex]n_2=3n_1[/tex]
Using above value in [2]
[tex]3n_1=\frac{P_2V_2}{RT_2}[/tex]
[tex]3\times \frac{P_1V_1}{RT_1}=\frac{P_2V_2}{RT_2}[/tex]
Given, [tex]P_1=P_2,T_1=T_2[/tex]
[tex]3\times \frac{P_2V_1}{RT_2}=\frac{P_2V_2}{RT_2}[/tex]
[tex]3V_1=V_2[/tex]
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.
