0.360 g of a diatomic gas occupies 125.0 mL at 23.0o C and 750. torr. What is the molar mass of the gas? What diatomic gas is it?

To solve this problem, we need to use the ideal gas law equation, which is PV = nRT. However, we need to find the molar mass, so we will rearrange the equation to solve for n (number of moles), which is n = PV/RT.

First, we need to convert the given values to the appropriate units:

• Pressure (P) is given in torr, but we need it in atmospheres. We know that 1 atm = 760 torr, so P = 750 torr * (1 atm / 760 torr) = 0.98684 atm.
• Volume (V) is given in mL, but we need it in liters. We know that 1 L = 1000 mL, so V = 125.0 mL * (1 L / 1000 mL) = 0.125 L.
• Temperature (T) is given in Celsius, but we need it in Kelvin. We know that T(K) = T(C) + 273.15, so T = 23.0 C + 273.15 = 296.15 K.
• R is the ideal gas constant, which is 0.0821 Latm/(Kmol).

Now we can substitute these values into the equation:

n = PV/RT = (0.98684 atm * 0.125 L) / (0.0821 Latm/(Kmol) * 296.15 K) = 0.00501 mol.

The molar mass of a substance is the mass of one mole of that substance. It is given by the formula:

Molar mass = mass / number of moles

Substituting the given mass (0.360 g) and the calculated number of moles (0.00501 mol), we get:

Molar mass = 0.360 g / 0.00501 mol = 71.86 g/mol.

This molar mass is close to the molar mass of chlorine gas (Cl2), which is 70.90 g/mol. Therefore, the diatomic gas is likely to be chlorine.