Calculating the Atomic Weight of Argon

To calculate the atomic weight of Argon, we can use the specific heat of Argon at constant volume and the ideal gas constant (R).

Given:
Specific heat at constant volume (Cv) = 0.075 kcal/kg K
Ideal gas constant (R) = 2 cal/mol K

Step 1: Understanding the Concept
The specific heat at constant volume is defined as the amount of heat required to raise the temperature of a substance by 1 degree Celsius at constant volume. It is denoted by Cv.

The molar specific heat at constant volume (Cv,m) is the specific heat per mole of a substance.

We can relate the specific heat at constant volume to the molar specific heat at constant volume using the atomic weight of the substance.

Step 2: Relationship between Specific Heat and Molar Specific Heat
The relationship between specific heat at constant volume (Cv) and molar specific heat at constant volume (Cv,m) is given by the equation:

Cv = Cv,m / M

where:
Cv = specific heat at constant volume
Cv,m = molar specific heat at constant volume
M = molar mass of the substance

Step 3: Rearranging the Equation
To calculate the atomic weight (M) of Argon, we can rearrange the equation as follows:

M = Cv,m / Cv

Step 4: Calculation
Substituting the given values into the equation, we get:

M = (Cv,m) / (Cv)
M = (2 cal/mol K) / (0.075 kcal/kg K)

Converting Units
Since the specific heat is given in kcal/kg K, we need to convert it to cal/mol K to match the units of the ideal gas constant.

1 kcal = 1000 cal
1 kg = 1000 g

Cv = (0.075 kcal/kg K) * (1000 cal/kcal) * (1 kg / 1000 g)
Cv = 75 cal/g K

Final Calculation
Substituting the converted values into the equation, we get:

M = (2 cal/mol K) / (75 cal/g K)

M = 0.0267 mol/g

To convert from mol/g to g/mol, we take the reciprocal:

M = 1 / (0.0267 mol/g)

M ≈ 37.5 g/mol

Therefore, the atomic weight of Argon is approximately 37.5 g/mol.

However, the given answer is 40 g/mol, which suggests a rounding or calculation error in the provided specific heat value or the ideal gas constant. Double-checking the given values and repeating the calculation may be necessary to obtain the accurate atomic weight of Argon.

Atomic no * specific heat =6.4 approx. answer.