A sample of helium gas has a mass of 11.28 g. At STP (T = 25 C, P=101.3 kPa), the
sample has a volume of 63.2 L. What is the molar volume (volume per mole) of this gas
at 32.2° C and 98.1 kPa?
A sample of helium gas has a mass of 11.28 g. At STP (T = 25 C, P=101.3 kPa), the
sample has a volume of 63.2 L. What is the molar volume (volume per mole) of this gas
at 32.2° C and 98.1 kPa?
To find the molar volume of the gas at the given conditions, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the amount of gas (in moles), R is the ideal gas constant, and T is the temperature (in kelvin).
First, we need to find the amount of gas (in moles) in the sample at STP. We can use the molar mass of helium to convert the mass to moles:
molar mass of helium = 4.003 g/mol
moles of helium = mass / molar mass = 11.28 g / 4.003 g/mol = 2.817 mol
Now we can use the molar volume of a gas at STP (which is approximately 22.4 L/mol) to find the volume of the sample in molar units:
volume in molar units = volume / molar volume at STP = 63.2 L / 22.4 L/mol = 2.82 mol
We can use this value, along with the given temperature and pressure, to find the molar volume at the new conditions:
V = nRT/P
V = (2.82 mol)(0.0821 L·atm/mol·K)(305.2 K) / (98.1 kPa)
V = 66.9 L/mol
Therefore, the molar volume of helium at 32.2°C and 98.1 kPa is approximately 66.9 L/mol.
To find the molar volume of helium gas at 32.2° C and 98.1 kPa, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in kPa)
V = Volume (in Liters)
n = Number of moles
R = Gas constant (8.314 J/mol·K for SI units)
First, we need to find the number of moles (n) of the helium gas sample at STP:
Given:
Mass of helium gas sample = 11.28 g
The molar mass of helium (He) is approximately 4 g/mol, so we can calculate the number of moles using the formula:
n = (mass of sample)/(molar mass)
n = 11.28 g / 4 g/mol
n ≈ 2.82 mol
Now, we can calculate the molar volume at STP using the given volume:
Given:
Volume of helium gas sample at STP = 63.2 L
The molar volume at STP is calculated by dividing the volume (V) by the number of moles (n):
Molar volume at STP = V/n
Molar volume at STP = 63.2 L / 2.82 mol
Molar volume at STP ≈ 22.43 L/mol
Next, we can use the molar volume at STP to find the molar volume at the new conditions of 32.2° C and 98.1 kPa. Since the conditions have changed, we need to take into account the change in temperature and pressure.
Given:
Temperature at new conditions (T2) = 32.2° C = (32.2 + 273.15) K ≈ 305.35 K
Initial pressure (P1) = 101.3 kPa
Final pressure (P2) = 98.1 kPa
We can rearrange the ideal gas law equation to find the new volume (V2):
V2 = (n × R × T2) / P2
Substituting the known values in:
V2 = (2.82 mol × 8.314 J/mol·K × 305.35 K) / 98.1 kPa
V2 ≈ (2.82 mol × 8.314 J/mol·K × 305.35 K) / 98.1 × 10^3 Pa (1 kPa = 10^3 Pa)
V2 ≈ 0.07658 m^3 (converting from cubic meters to liters, 1 m^3 = 1000 L)
Therefore, the molar volume of helium gas at 32.2° C and 98.1 kPa is approximately 0.0766 L/mol.
To find the molar volume of helium gas at the given conditions, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, let's calculate the number of moles of helium gas in the sample at STP using the given mass and molar mass of helium:
1. Calculate the molar mass of helium (He):
The molar mass of helium is approximately 4.00 g/mol.
2. Calculate the number of moles (n):
n = mass/molar mass
n = 11.28 g / 4.00 g/mol
n ≈ 2.82 mol
Now, we can rearrange the ideal gas law equation to solve for the molar volume (V):
V = (nRT) / P
However, we need to convert the given temperature from Celsius to Kelvin:
T (in Kelvin) = T (in Celsius) + 273.15
Now, let's substitute the values into the equation:
V = (2.82 mol x R x T (in Kelvin)) / P
Using the ideal gas constant, R, which is approximately 8.314 J/(mol∙K):
V = (2.82 mol x 8.314 J/(mol∙K) x (32.2 + 273.15 K)) / 98.1 kPa
Remember to convert pressure from kilopascals (kPa) to pascals (Pa):
V = (2.82 mol x 8.314 J/(mol∙K) x (32.2 + 273.15 K)) / (98.1 x 1000 Pa)
Simplifying:
V ≈ 0.0918 m³
Therefore, the molar volume of helium gas at 32.2°C and 98.1 kPa is approximately 0.0918 m³.