Final answer:
Using the Ideal Gas Law, the molar mass of freon-113 in the given conditions is calculated to be approximately 121.6 g/mol. Option A is correct.
Step-by-step explanation:
The question asks for the molar mass of freon-113 gas when 1.018 g of the gas is trapped in a 175 ml container at 760 mmHg and 50.0°C. To find the molar mass, we can start by converting 175 ml to liters, since standard gas equations use liters, 175 ml is equivalent to 0.175 L. Next, since we are using mmHg as our pressure unit and we have the temperature in °C, it's convenient to use the Ideal Gas Law in the following form:
PV = nRT, where P is the pressure in mmHg, V is the volume in liters, n is the number of moles, R is the ideal gas constant in L mmHg / (mol K), and T is the temperature in Kelvin.
Firstly, we need to convert the temperature to Kelvin: T(K) = 50.0 °C + 273.15 = 323.15 K.
Next, we need the value for R that matches our other units: R = 62.364 L mmHg / (mol·K). Now, we can rearrange the Ideal Gas Law to solve for n (the number of moles):
n = PV / RT
n = (760 mmHg × 0.175 L) / (62.364 L mmHg / (mol·K) × 323.15 K)
n ≈ 0.00837 moles
Now, we can calculate the molar mass (M) of the gas:
M = mass of gas / number of moles
M = 1.018 g / 0.00837 moles
M ≈ 121.6 g/mol
Since 121.6 g/mol is not exactly one of the given options but is closest to 122.4 g/mol, we can surmise that there may be a slight rounding difference or experimental error. Thus the best answer, based on our calculation, would be: a) 122.4 g/mol.
The given options do not match exactly, so the closest provided option, 122.4 g/mol, is likely the correct answer, allowing for small variances in the true molar mass or rounding errors in the calculation.