the gaseous product of a reaction is collected in a 25.0L container at 27c. the pressure in the container is 300.0 kpa and the gas has a mass of 96.0g. what is the molar mass of the gas?
To find the molar mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in Pascals)
V = volume (in cubic meters)
n = number of moles
R = ideal gas constant (8.314 J/mol·K)
T = temperature (in Kelvin)
To solve this problem, we need to convert the given values to the appropriate units:
First, convert the temperature from Celsius to Kelvin:
T = 27°C + 273.15 = 300.15 K
Next, convert the volume from liters to cubic meters:
V = 25.0 L * (1 m^3 / 1000 L) = 0.025 m^3
Now, let's rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substitute the given values into the equation:
n = (300,000 Pa) * (0.025 m^3) / ((8.314 J/mol·K) * (300.15 K))
Calculating using the given values:
n = 300000 * 0.025 / (8.314 * 300.15) = 3.006 mol
Now that we have the number of moles (n), we can find the molar mass (M) using the formula:
M = mass / n
Substituting the values:
M = 96.0 g / 3.006 mol
Calculating:
M ≈ 31.9 g/mol
Therefore, the molar mass of the gas is approximately 31.9 g/mol.
To determine the molar mass of the gas, we first need to calculate the number of moles of gas using the Ideal Gas Law equation:
PV = nRT
Where:
P = Pressure (in kPa)
V = Volume (in liters)
n = Number of moles
R = Ideal Gas Constant (8.314 J/mol·K)
T = Temperature (in Kelvin)
Let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 27°C + 273.15 = 300.15 K
Now we can rearrange the Ideal Gas Law equation to solve for the number of moles:
n = PV / RT
n = (300.0 kPa * 25.0 L) / (8.314 J/mol·K * 300.15 K)
n ≈ 31.7506 mol
Next, we calculate the molar mass using the formula:
Molar mass (grams/moles) = Mass (grams) / Moles
Molar mass ≈ 96.0 g / 31.7506 mol = 3.021 g/mol
Hence, the molar mass of the gas is approximately 3.021 g/mol.
PV=nRT
PV= mass/molemass*RT
solve for mole mass. Watch the units for R, make certain they match your measurement units.