Methane gas, CH4, is sold in a 43.0L cylinder containing 5.91kg .What is the pressure inside the cylinder (in kilopascals) at 21∘C?
Use PV = nRT
P in kPa
V in L
n = grams/molar mass
R = 8.314
T = kelvin = 273+C
To find the pressure inside the cylinder, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in units of force per unit area, such as Pascals or kilopascals)
V = volume (in liters)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 21°C + 273.15
T(K) = 294.15 K
Next, we need to find the number of moles of methane gas (CH4) inside the cylinder. To do this, we'll use the relationship between mass, molar mass, and moles:
moles = mass (in kg) / molar mass (in kg/mol)
The molar mass of methane is 16.04 g/mol, so we need to convert the given mass from kg to grams:
mass(g) = mass(kg) x 1000
mass(g) = 5.91 kg x 1000
mass(g) = 5910 g
Now we can use the moles and the ideal gas law equation to find the pressure:
PV = nRT
First, we need to convert the given volume from liters to m^3:
V(m^3) = V(L) / 1000
V(m^3) = 43.0 L / 1000
V(m^3) = 0.043 m^3
Now, we can substitute the values into the equation and solve for P:
P(V) = (moles * R * T) / V
P = (moles * R * T) / V
P(kPa) = (moles * R * T) / (V * 1000)
P(kPa) = (moles * R * T) / (V * 1000)
P(kPa) = (mass(g) / molar mass(g/mol)) * R * T / (V * 1000)
Substituting the given values:
P(kPa) = (5910 g / 16.04 g/mol) * (8.314 J/(mol⋅K)) * (294.15 K) / (0.043 m^3 * 1000)
P(kPa) ≈ 107050.62 kPa
Therefore, the pressure inside the cylinder at 21°C is approximately 107050.62 kilopascals.
To find the pressure inside the cylinder, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure in kilopascals (kPa)
V is the volume in liters (L)
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/mol·K or 8.314 J/mol·K)
T is the temperature in Kelvin (K)
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273
T(K) = 21 + 273
T(K) = 294 K
Next, we need to calculate the number of moles of methane gas:
n = mass / molar mass
The molar mass of methane (CH4) can be calculated as follows:
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol
Molar mass of CH4 = 12.01 g/mol + (1.01 g/mol * 4) = 16.05 g/mol
Given mass of CH4 = 5.91 kg = 5910 g
n = 5910 g / 16.05 g/mol = 367.9 mol
Now we can substitute the values into the ideal gas law equation:
PV = nRT
P * 43.0 L = 367.9 mol * (0.0821 L·atm/mol·K) * 294 K
Solving for P:
P = (367.9 * 0.0821 * 294) / 43.0
P ≈ 1609.2 kPa
Therefore, the pressure inside the cylinder is approximately 1609.2 kilopascals (kPa) at 21∘C.