Answer:
Assuming ideal gas behavior, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperature from Celsius to Kelvin:
T = 313 ºK
The gas constant R is 8.31 J/(mol·K), but we need to use a value in units of kPa·L/(mol·K) for the pressure and volume units given:
R = 8.31 kPa·L/(mol·K)
Plugging in the given values, we have:
P × 20.0 L = 10.0 mol × 8.31 kPa·L/(mol·K) × 313 K
Solving for P, we get:
P = (10.0 mol × 8.31 kPa·L/(mol·K) × 313 K) / 20.0 L
P = 1293 kPa
Therefore, the final pressure in the cylinder is 1293 kPa.