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

(a) The molar mass of oxygen is $M(O_2) = 2 \cdot M(O) = 2 \cdot 16 = 32$ g/mol. To find the amount of substance we need to divide mass by molar mass

$n = \frac{m}{M}=\frac{12}{32}=0.375$ mol.

(b) The gas is heated at constant pressure. By definition, $C_p = (\frac{\delta Q}{dT})_P$. Also, we know that $C_P = \frac{i+2}{2}R$, where i is a number of degrees of freedom, R is universal gas constant. i = 5 (3 translation + 2 rotation, molecules do not vibrate). For n moles of substance we obtain

$\Delta Q = n \cdot C_P \Delta T = \frac{7}{2} nR \Delta T = 3.5 \cdot 0.375 \cdot 8.314 \cdot 100= 1091$ J.

(c) Assuming we have an ideal gas, $dU = nC_VdT$ , $C_V = \frac{i}{2}R$ .

$\Delta U = \frac{5}{2}nR\Delta T$

$\frac{\Delta U}{\Delta Q} = \frac{\frac{5}{2}nR\Delta T}{\frac{7}{2}nR\Delta T} = \frac{5}{7}$

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