Question

Consider a gas sample of 12 g of oxygen (O_2) in a container, and it is heated at constant pressure, and when heated its temperature increases from 25⁰C to 125⁰C. (a) Calculate number of moles of oxygen present, (b) How much energy is transferred to oxygen gas as heat, keeping in mind that molecules rotate but do not vibrate. (c) What fraction of the heat is used to increase the internal energy of the oxygen?

Answer 1

(а) n=m/M

$n(O_{2}) = 12 g / (32 g/mol) = 0.375 mol$

(b) Molar specific heat of a diatomic gas (number of degrees of freedom = 5 [3 translation + 2 rotation], assuming molecules do not vibrate) at constant pressure C_p = \frac{7}{2}R

R is gas constant.

$R = 8.314 J/Kmol$

$C_{p}(O_{2}) = \frac{7}{2}\times8.314 = 29.099 J/Kmol$

$ΔQ=n\times C_{p}\timesΔT$

ΔT = 100 K

$ΔQ=0.375 mol \times 29.099 J/Kmol \times 100 K = 1091.21 J$  

ΔQ = 1.09 kJ

(c) Change in internal energy of $O_{2}$ at constant volume:

$ΔU=n\times C_{v}\timesΔT$

$C_{v}=\frac{5}{2}R$

Ratio ΔU/ΔQ = (n$\times\frac{5}{2}$ R$\times$ ΔT)/(n$\times\frac{7}{2}$ R$\times$ ΔT) = $\frac{5}{7}$

$\frac{5}{7}$ fraction of heat supplied is used to increase the internal energy of the oxygen.