Gas Specific Heat and Atom Mass Calculation

How can we calculate the mass of a monoatomic gas based on its specific heat at constant volume?

Given the specific heat at constant volume cV = 0.075 cal/g · C° for a gas, how can we determine the mass of its atom and molar mass?

Answer:

a) The mass of the atom is 6.6*10^-23 g

b) The molar mass is 39.74 g/mol

When dealing with a monoatomic gas, the specific heat at constant volume cV can be utilized to calculate various properties. In this case, cV is given as 0.075 cal/g · C° for the gas. To determine the mass of its atom, we need to consider the molar specific heat at constant volume CV.

If the monoatomic gas behaves as an ideal gas, we can find that CV = 3/2 R, where R is the universal gas constant. By substituting the value of R (1.987 cal/mol*K), we get CV as 2.9805 cal/mol*K. This leads us to the equation Q = m cV ΔT = n CV ΔT, where m represents the mass and n is the number of moles.

By rearranging the equation and solving for molar mass (M = m/n), we have M = CV / cV. Thus, the molar mass is calculated as M = 2.9805 / 0.075 = 39.74 g/mol. Additionally, with Avogadro's number (6.022*10^23 mol^-1), we can compute the atom mass as mAtom = M / NAv.

Therefore, the mass of the atom is determined as mAtom = 39.74 / 6.022*10^23 = 6.6*10^-23 g, showcasing the significance of specific heat in analyzing the properties of monoatomic gases.