Question

A gas sample containing 1.50 mol at 25°C exerts a pressure of 400 torr. Some gas is added to the container and the temperature is increased by 25°C. If the pressure increases to 800 torr, how many moles of gas must have been added to the container, assuming the volume hasn't changed?

Answer 1

To solve this problem, we use the ideal gas law and the given values of pressure, volume, and temperature. Using the equation P1V1/n1T1 = P2V2/n2T2, we can calculate the number of moles of gas added to the container. The answer is 3.00 moles.

Step-by-step explanation:

To solve this problem, we can use the ideal gas law, which states that PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in kelvin. Since the volume hasn't changed, we can set up the equation:

P1V1/n1T1 = P2V2/n2T2

Given that P1 = 400 torr, n1 = 1.50 mol, T1 = 25°C + 273.15 = 298.15 K, P2 = 800 torr, T2 = (25°C+25°C) + 273.15 = 323.15 K, and V1 = V2, we can solve for n2:

n2 = (P2 * n1 * T1)/(P1 * T2)

Substituting the values, we get n2 = (800 torr * 1.50 mol * 298.15 K)/(400 torr * 323.15 K) = 3.00 mol.