What is the pressure inside a 33.1 L container holding 109.1 kg of argon gas at 399 K?
To find the pressure inside the container, we can use the ideal gas law, which states:
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)
First, we need to convert the given volume from liters to cubic meters:
33.1 L = 0.0331 m^3
Next, we need to calculate the number of moles of argon gas. We can use the molar mass of argon to convert from kilograms to moles:
Molar mass of argon (Ar) = 39.948 g/mol
109.1 kg = 109,100 g
109,100 g / 39.948 g/mol = 2,732.6 moles
Now, we can plug these values into the ideal gas law equation:
PV = nRT
P * 0.0331 m^3 = 2,732.6 moles * 8.314 J/(mol·K) * 399 K
Simplifying the equation:
P = (2,732.6 * 8.314 * 399) / 0.0331
Calculating the pressure:
P = 81,958,269 Pa
Therefore, the pressure inside the 33.1 L container holding 109.1 kg of argon gas at 399 K is approximately 81,958,269 pascals.
To calculate the pressure inside a container, we can use the ideal gas law equation, which states: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's calculate the number of moles of argon gas in the container. We can use the formula: n = m/M, where n is the number of moles, m is the mass of the gas, and M is the molar mass of argon.
The molar mass of argon (Ar) is approximately 39.95 g/mol.
m = 109.1 kg × 1000 g/kg = 109,100 g
n = 109,100 g / 39.95 g/mol
Next, we need to convert the volume from liters to cubic meters, as SI units are required for the ideal gas law.
V = 33.1 L × (1 m^3 / 1000 L)
Now, we can substitute the values into the ideal gas law equation:
PV = nRT
P × (V) = (n) × (R) × (T)
P = (n × R × T) / V
R is the ideal gas constant, approximately 8.314 J/(mol·K).
T is the temperature in Kelvin, given as 399 K.
Substituting the values:
P = (n × 8.314 J/(mol·K) × 399 K) / V
Lastly, plug in the calculated values to find the pressure:
P = (n × 8.314 J/(mol·K) × 399 K) / 33.1 L
By evaluating this expression, you can determine the pressure inside the container holding 109.1 kg of argon gas at 399 K.