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

a)
`6.6*10^(-23)g`

b) 39.74 g/mol

Step-by-step 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)=(3)/(2) R` with R the universal gas constant. So
   `C_(V)= (3)/(2) (1.987 (cal)/(mol*K))=2.9805 (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 = (m)/(n) = (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) = (M)/(N_(Av) )`
6. Answer for the question a) is
   `m_(atom) =(39.74)/(6.022*10^(23) )=6.6*10^(-23)g`