If a 2.15-g sample of gas occupies 750. mL at STP, what is the molar mass of the gas at 125 degrees celcuis
To determine the molar mass of a gas, we can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Given:
Mass of gas (m) = 2.15 g
Volume of gas (V) = 750 mL = 0.750 L
Temperature (T) = 125 °C
To start, we need to convert the temperature from Celsius to Kelvin.
T(K) = T(°C) + 273.15
Therefore:
T(K) = 125 + 273.15 = 398.15 K
Now, let's rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Since the gas is at STP (standard temperature and pressure), the pressure (P) is 1 atm, and the gas constant (R) is 0.0821 L·atm/(mol·K).
Plugging in the values:
n = (1 atm) * (0.750 L) / (0.0821 L·atm/(mol·K) * 398.15 K)
Simplifying:
n ≈ 0.0220 mol
Now, we can calculate the molar mass (M) using the equation:
M = mass / n
M = 2.15 g / 0.0220 mol
M ≈ 97.73 g/mol
Therefore, the molar mass of the gas at 125 degrees Celsius is approximately 97.73 g/mol.