If a nitrogen gas sample occupies a volume of 2.55 L at 22.0 degrees Celsius and 0.860 atm, what is the mass of the N2 gas?
PV=nRT
n=PV/RT
n=0.860*2.55/0.08206*(22.0+273.15)
n=2.19/24.2
n=0.0906 mole
0.0906molN*28.00g N/1 mole N
N=2.54g of N2
Use PV = nRT and solve for n = number of moles.
Then n = grams/molar mass and solve for grams. You know the molar mass N2 = about 28
To determine the mass of the N2 gas, we need to use the Ideal Gas Law equation:
PV = nRT
where:
P is the pressure of the gas in atm,
V is the volume of the gas in liters,
n is the number of moles of the gas,
R is the ideal gas constant (0.0821 L·atm/mol·K),
and T is the temperature of the gas in Kelvin.
First, let's convert the given temperature from degrees Celsius to Kelvin:
T(K) = T(C) + 273.15
T(K) = 22.0 + 273.15
T(K) = 295.15 K
Now, let's rearrange the Ideal Gas Law equation to solve for n, the number of moles of the gas:
n = PV / RT
n = (0.860 atm) * (2.55 L) / (0.0821 L·atm/mol·K) * (295.15 K)
n ≈ 0.1004 moles of N2 gas
Next, we need to calculate the molar mass of N2, which is the sum of the atomic masses of nitrogen (N):
Molar mass of N2 = 2 * Molar mass of N
The atomic mass of nitrogen (N) is approximately 14.0 g/mol.
Molar mass of N2 = 2 * 14.0 g/mol
Molar mass of N2 = 28.0 g/mol
Finally, we can calculate the mass of the N2 gas using the formula:
Mass = number of moles * molar mass
Mass = 0.1004 moles * 28.0 g/mol
Mass ≈ 2.810 g
Therefore, the mass of the N2 gas is approximately 2.810 grams.
To calculate the mass of the N2 gas sample, 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.
First, convert the temperature from Celsius to Kelvin by adding 273.15:
T = 22.0 + 273.15 = 295.15 K
Rearrange the Ideal Gas Law equation to solve for n (moles):
n = PV / RT
Plug in the given values:
P = 0.860 atm
V = 2.55 L
R = 0.0821 L·atm/(mol·K)
T = 295.15 K
n = (0.860 atm * 2.55 L) / (0.0821 L·atm/(mol·K) * 295.15 K)
n = 0.0903 moles of N2 gas
Next, calculate the molar mass of N2. Nitrogen (N) has an atomic mass of 14.01 g/mol, and since N2 has two nitrogen atoms, the molar mass of N2 is:
Molar Mass (N2) = 2 * Molar Mass (N)
Molar Mass (N2) = 2 * 14.01 g/mol
Molar Mass (N2) = 28.02 g/mol
Finally, we can calculate the mass of the N2 gas sample using the equation:
Mass (g) = moles * Molar Mass
Mass (N2) = 0.0903 moles * 28.02 g/mol
Mass (N2) = 2.53 g
Therefore, the mass of the N2 gas sample is 2.53 grams.