Question

methanol (CH₃OH) can be synthesized by the following reaction: CO(g)+2H₂(g)--->CH₃OH(g)

what volume (in liters) of hydrogen gas, at a temperature of 355 K and a pressure of 738 mm Hg, is required to synthesize 35.7g of methanol?

Answer 1

Molar mass of CH₃OH is = 12 + (3x1) + 16 + 1 = 32 g/mol

Given mass of CH₃OH synthesized is , m = 35.7 g

So number of moles of methanol , CH₃OH , n = mass / molar mass

                                                                   = 35.7 g / 32 (g/mol)

                                                                   = 1.116 mol                                                                 

CO(g)+2H₂(g) CH₃OH(g)

According to the above balanced equation ,

1 mole of CH₃OH systhesized from 2 moles of H₂ gas

1.116 mole of CH₃OH systhesized from 2x1.116=2.232 moles of H₂ gas

Calculation of Volume of H₂ gas :-

We know that PV = nRT

Where

T = Temperature = 355 K

P = pressure = 738 mm Hg = 738 / 760 atm                  Since 1 atm = 760 mm Hg

                                        = 0.97 atm

n = No . of moles = 2.232 moles

R = gas constant = 0.0821 L atm / mol - K

V= Volume of the gas = ?

Plug the values we get

Therefore the volume of hydrogen gas required is 67 L