Question

In the fermentation of glucose (wine making),

750 mL of CO2 gas was produced at 37 ∘C and 1.00 atm .

What is the final volume, in liters, of the gas when measured at 24 ∘C and 655 mmHg , when n is constant?

Answer 1

First calcule mole of CO₂ gas produced

Use ideal gas equation for calculation of mole of gas

Ideal gas equation

PV = nRT             where, P = atm pressure= 1.0 atm,

V = volume in Liter = 750 ml = 0.750 L

n = number of mole = ?

R = 0.08205L atm mol^-1 K^-1 =Proportionality constant = gas constant,

T = Temperature in K = 37⁰C = 273.15+ 37 = 310.15 K

We can write ideal gas equation

n = PV/RT

Substitute the value

n = (1.0 X 0.750)/(0.08205 X 310.15) = 0.029472 mole

now calculte volume of gas at 24⁰C and 655 mm Hg

We know that PV = nRT

V = nRT/P

n = 0.029472mole,

T = 24⁰C = 24+273.15 = 297.15K,

P= 655 mmHg = 0.8615 atm,

R = 0.08205 L atm mol^-1 K^-1 ( R = gas constant)

V = ?

Substitute these value in above equation.

V = 0.029472 X 0.08205 X 297.15/0.8615 = 0.834 L

Final volue of CO₂ gas = 0.834 L