Question

Methanol can be formed by the catalytic reaction of hydrogen and carbon monoxide as shown below. How much heat is released when 15.0 L of CO at 85°C and 112 kPa reacts with 18.5 L of H2 gas at 75°C and 744 torr?

Answer 1

Calculation of number of moles of CO :

We know that PV = nRT

Where

T = Temperature = 85 oC = 85+273 = 358 K

P = pressure = 112 KPa = 112x0.00987 atm               Since 1 atm = 0.00987 atm

= 1.105 atm

n = No . of moles = ?

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

V= Volume of the gas = 15.0 L

Plug the values we get n = 0.564 moles

Calculation of number of moles of H2 :

We know that PV = nRT

Where

T = Temperature = 75 oC = 75+273 = 348 K

P = pressure = 744 torr atm               Since 1 atm = 760 torr

= 0.980 atm

n = No . of moles = ?

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

V= Volume of the gas = 18.5 L

Plug the values we get n = 0.634 moles

The balanced reaction is CO(g) + 2H₂(g) CH₃OH(l) : H = -128.1 kJ   ---(1)

According to the balanced equation ,

1 mole of CO reacts with 2 moles of H₂

M mole of CO reacts with 0.634 moles of H₂

M = (1x0.634) / 2

    = 0.317 mol

So 0.564-0.317 moles of CO left unreacted , CO is the excess reactant

Since all the mass of H2 completly reacted it is the limiting reactant

From the reaction

2 moles of H2 on reaction produces 128.1 kJ of heat

0.634 moles of H2 on reaction produces N kJ

N = ( 0.634x128.1) / 2

   = 40.6 kJ

Therefore the amount of heat released is 40.6 kJ