Question

A sample of oxygen gas with a mass of 46.0 g is contained in a 175 ml, flexible container at a particular temperature and pressure. If 10.0 g of the gas leaks out, what is the volume of the container at the same temperature and pressure

Answer 1

To find the volume of the container after the gas leaks out, we can use the Ideal Gas Law equation PV = nRT. By using the given mass of the leaked gas and the molar mass of oxygen, we can find the number of moles that leaked out. Finally, we can use the Ideal Gas Law equation again to find the new volume. The new volume of the container is 122ml or 0.122Liter.

Step-by-step explanation:

To solve this problem, we can use the concept of the Ideal Gas Law. The Ideal Gas Law equation is 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. Since the temperature and pressure remain constant, we can use the equation PV = nRT to find the initial number of moles of oxygen. Then, we can use the mass of the leaked gas to find the number of moles that leaked out.

Finally, we can use the equation PV = nRT again to find the new volume.

First, let's find the initial number of moles of oxygen. We can rearrange the Ideal Gas Law equation to solve for n:

n = PV / RT

Plugging in the given values, we have:

n = (764 torr)(0.560 L) / (0.08206 L.atm/mol.K)(302.15 K)

= 1.08 moles

Next, let's find the number of moles that leaked out.

We can use the mass of the leaked gas and the molar mass of oxygen to find the number of moles:

mass = n * molar mass

10.0 g = n * 32.00 g/mol

n = 0.3125 moles

Finally, let's find the new volume. We can rearrange the Ideal Gas Law equation to solve for V:

V = nRT / P

Plugging in the values we found, we have:

V = (0.3125 moles)(0.08206 L.atm/mol.K)(302.15 K) / (764 torr)

= 0.122 L or 122 mL