Question

A glass container was initially charged with 1.80 moles of a gas sample at 4.25 atm and 21.7 °c. some of the gas was released as the temperature was increased to 30.1 °c, so the final pressure in the container was reduced to 1.25 atm. how many moles of the gas sample are present at the end?

Answer 1

To determine the number of moles of gas remaining after conditions in the container change, the combined gas law is used. The initially present 1.80 moles of gas undergo a pressure and temperature change, which is accounted for to solve for the final number of moles.

Step-by-step explanation:

To calculate the number of moles of gas remaining in the container after some gas is released and the temperature is increased, we can use the ideal gas law equation: PV = nRT. However, since we're comparing initial and final conditions, and the volume and the gas constant (R) don't change, we can set up a ratio using the combined gas law: (P1 x V1) / (T1) = (P2 x V2) / (T2). Since the volume remains the same, it cancels out, and we are left with (P1 / T1) = (n1 / n2) x (P2 / T2).

Originally, the container held 1.80 moles of the gas at 4.25 atm and 294.85 K (21.7 °C in Kelvin). The final pressure after releasing some of the gas is 1.25 atm, and the final temperature is 303.25 K (30.1 °C in Kelvin). Using the combined gas law, we solve for n2, the number of moles at end:

Initial state: (P1 / T1) = (4.25 atm / 294.85 K)

Final state: (n2 x 1.25 atm) / 303.25 K.

After equating the two states and solving for n2, we can find the final number of moles present in the container.