The density of an unknown gas is 1.72 g/L at 750.0 torr and 30.0°C. Which of the following could be the unknown gas?
a. CS2
b. NO
c. N2O
d. NH3
e. N02
To determine which of the following gases could be the unknown gas based on the given information, we need to calculate the molar mass of each gas and compare it to the known molar masses.
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 30.0 + 273.15
T(K) = 303.15 K
Next, we can use the Ideal Gas Law equation to calculate the molar mass of each gas:
PV = nRT
Since we are given the density (d), we can use the formula:
d = m/V, where m is the mass and V is the volume.
Rearranging the equation, we get:
PV = (m/M)(RT), where M is the molar mass.
Rearrange the equation to solve for molar mass (M):
M = (mRT)/PV
Now we can calculate the molar mass for each gas:
a. CS2 (Carbon disulfide)
The molar mass of CS2 is approximately 76.14 g/mol.
b. NO (Nitric oxide)
The molar mass of NO is approximately 30.01 g/mol.
c. N2O (Dinitrogen monoxide or Nitrous oxide)
The molar mass of N2O is approximately 44.01 g/mol.
d. NH3 (Ammonia)
The molar mass of NH3 is approximately 17.03 g/mol.
e. N02 (Nitrogen dioxide)
The molar mass of N02 is approximately 46.01 g/mol.
Now, let's calculate the molar mass for each gas using the given information:
For gas a. CS2:
M = (1.72 g/L * 0.0821 L.atm/mol.K * 303.15 K) / 750.0 torr
M = (1.72 * 0.0821 * 303.15) / 750.0
M ≈ 7.01 g/mol
For gas b. NO:
M = (1.72 g/L * 0.0821 L.atm/mol.K * 303.15 K) / 750.0 torr
M = (1.72 * 0.0821 * 303.15) / 750.0
M ≈ 7.01 g/mol
For gas c. N2O:
M = (1.72 g/L * 0.0821 L.atm/mol.K * 303.15 K) / 750.0 torr
M = (1.72 * 0.0821 * 303.15) / 750.0
M ≈ 7.01 g/mol
For gas d. NH3:
M = (1.72 g/L * 0.0821 L.atm/mol.K * 303.15 K) / 750.0 torr
M = (1.72 * 0.0821 * 303.15) / 750.0
M ≈ 7.01 g/mol
For gas e. N02:
M = (1.72 g/L * 0.0821 L.atm/mol.K * 303.15 K) / 750.0 torr
M = (1.72 * 0.0821 * 303.15) / 750.0
M ≈ 7.01 g/mol
From the calculations, we can see that the molar mass for each gas is approximately 7.01 g/mol. Since all the molar masses are the same, any of the given gases (a, b, c, d, or e) could be the unknown gas.
To determine which gas could be the unknown gas based on the given information, we can calculate the molar mass of each gas in order to compare with the density value.
The ideal gas law relates the pressure, volume, temperature, and molar mass of a gas, and it can be written as:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature
Rearranging the equation to solve for n (number of moles), we get:
n = PV / RT
Now, the molar mass (M) of a gas can be calculated using the equation:
M = m / n
Where:
M = molar mass
m = mass (in grams) of the gas
n = number of moles of the gas
To calculate the molar mass of each gas, we need to rearrange the equation as:
m = M * n
Given that the density of the gas is 1.72 g/L, we can calculate the mass of 1 mole of gas by multiplying the density by the molar volume:
m = density * (1 L / Molar Volume)
The molar volume at STP (Standard Temperature and Pressure) is 22.4 L/mol.
Now, we can calculate the mass (m) of each gas:
For CS2:
density = 1.72 g/L
m = 1.72 g/L * (1 L / 22.4 L/mol)
M = 76.14 g/mol
For NO:
density = 1.72 g/L
m = 1.72 g/L * (1 L / 22.4 L/mol)
M = 30.01 g/mol
For N2O:
density = 1.72 g/L
m = 1.72 g/L * (1 L / 22.4 L/mol)
M = 44.02 g/mol
For NH3:
density = 1.72 g/L
m = 1.72 g/L * (1 L / 22.4 L/mol)
M = 17.03 g/mol
For N2O2:
density = 1.72 g/L
m = 1.72 g/L * (1 L / 22.4 L/mol)
M = 46.02 g/mol
Now, we compare the calculated molar masses (M) with the known molar masses of the gases to determine which gas could be the unknown gas:
a. CS2 - M = 76.14 g/mol
b. NO - M = 30.01 g/mol
c. N2O - M = 44.02 g/mol
d. NH3 - M = 17.03 g/mol
e. N2O2 - M = 46.02 g/mol
Comparing the calculated molar masses with the known molar masses, we find that NH3 (ammonia) has a molar mass of approximately 17.03 g/mol, which matches the calculated molar mass based on the given density. Therefore, the unknown gas is most likely ammonia (NH3).
The correct answer is d. NH3.
p*molar mass = density*RT
Solve for molar mass and compare with those listed.