Question

The mass of a monoatomic gas can be computed from its specific heat at constant volume cV. (Note that this is not CV.) Take cV = 0.075 cal/g · C° for a gas and calculate (a) the mass of its atom and (b) the molar mass.

Answer 1

Answer:

a) $6.6*10^{-23}g$

b) 39.74 g/mol

Explanation:

1. We have specific heat at constant volume $c_{V} = 0.075$ cal/g
2. if the monoatomic gas behaves as ideal gas, we can know the molar specific heat at constant volume $C_{V}$ . For a monoatomical gas $C_{V}=\frac{3}{2} R$ with R the universal gas constant. So $C_{V}= \frac{3}{2} (1.987 \frac{cal}{mol*K})=2.9805 \frac{cal}{mol*K}[$.
3. We can calculate the heat with $c_{V}$ or $C_{V}$ as follows $Q= m c_{V} \Delta T = n C_{V} \Delta T$ with m: mass and n: number of moles. So we can solve that equation for the molar mass (M=m/n) obtaining $M = \frac{m}{n} = \frac{C_{V} }{c_{V} }$.
4. We can answer the question b) M=2.9805/0.075=39.74 g/mol
5. With the molar mass and the avogadro's number ($N_{Av}=6.022*10^{23}$ $mol^{-1}$ we can calculate the atom mass as follows $m_{atom} = \frac{M}{N_{Av} }$
6. Answer for the question a) is $m_{atom} =\frac{39.74}{6.022*10^{23} }=6.6*10^{-23}g$