A gas cylinder has a volume on 200l, and contains Nitrogen at a pressure of 200kPa and a temperature of 290 degrees Kelvin. The molar mass of Nitrogen is 14.0067g. Calculate.
The number of moles in the gas cylinder?
To calculate the number of moles in the gas cylinder, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in Pa)
V = volume (in m^3)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given values into the appropriate units:
Pressure (P) = 200 kPa = 200,000 Pa
Volume (V) = 200 L = 0.2 m^3 (since 1 L = 0.001 m^3)
Temperature (T) = 290 Kelvin
Now, we can plug in the values into the ideal gas law equation:
200,000 Pa * 0.2 m^3 = n * 8.314 J/(mol·K) * 290 K
Solving for n, the number of moles:
n = (200,000 Pa * 0.2 m^3) / (8.314 J/(mol·K) * 290 K)
n ≈ 16.843 moles
Therefore, the number of moles in the gas cylinder is approximately 16.843 moles.
To calculate the number of moles in the gas cylinder, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas in pascals (Pa)
V = volume of the gas in cubic meters (m³)
n = number of moles of the gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas in Kelvin (K)
First, we need to convert the given values to their appropriate units.
The volume is given as 200 liters, so we convert it to cubic meters:
200 liters = 200 x (1/1000) m³ = 0.2 m³
The pressure is given as 200 kPa, so we convert it to pascals:
200 kPa = 200 x 1000 Pa = 200,000 Pa
The temperature is given as 290 degrees Kelvin, which is already in the correct unit.
Now, we can plug the values into the equation:
(200,000 Pa) * (0.2 m³) = n * (8.314 J/(mol·K)) * (290 K)
Simplifying the equation:
40,000 = 2379.46n
Now, solve for n:
n = 40,000 / 2379.46 ≈ 16.82 moles
Therefore, the number of moles in the gas cylinder is approximately 16.82 moles.