A 10-g mass of krypton occupies 15.0 L at a pressure of 210 kPa. Find the volume of the krypton when the pressure is increased to 790 kPa.
The 10 g mass is extraneous information. You don't need it.
P1V2 = P2V2.
okay. The 10 g mass was throwing me off.
To find the volume of krypton when the pressure is increased to 790 kPa, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law Equation:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
P2 = final pressure of the gas
V2 = final volume of the gas
We are given the following information:
P1 = 210 kPa
V1 = 15.0 L
P2 = 790 kPa
Now we can substitute the values into the equation and solve for V2:
P1 * V1 = P2 * V2
210 kPa * 15.0 L = 790 kPa * V2
Divide both sides of the equation by 790 kPa:
(210 kPa * 15.0 L) / 790 kPa = V2
Calculate:
V2 = 3.98 L
Therefore, the volume of krypton when the pressure is increased to 790 kPa is approximately 3.98 L.
To solve this problem, we can use the ideal gas law formula: PV = nRT, where P represents pressure, V represents volume, n represents the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Since we're dealing with a krypton gas, we know its molecular mass is 83.80 g/mol.
First, we need to find the number of moles of krypton in the given 10 g of krypton. We can use the formula:
n = m/M
where n is the number of moles, m is the mass, and M is the molar mass.
n = 10 g / 83.80 g/mol
n ≈ 0.1193 mol (rounded to four decimal places)
Now, let's use the ideal gas law to find the initial volume of the krypton:
PV = nRT
V = nRT / P
Since the problem provides the pressure (210 kPa), we can use this value to calculate the initial volume. However, we need to convert the pressure to Pascal (Pa) and the volume to cubic meters (m^3) to ensure consistent units:
P = 210 kPa = 210,000 Pa
V = 15.0 L = 0.015 m^3
Plugging the values into the equation:
V = (0.1193 mol * 8.314 J/(mol·K) * 298 K) / 210,000 Pa
V ≈ 0.0026 m^3 (rounded to four decimal places)
Now, we can use the volume and pressure information to calculate the final volume:
V = nRT / P
However, this time the pressure is increased to 790 kPa. Let's convert the pressure to Pascal (Pa):
P = 790 kPa = 790,000 Pa
Now we can solve for the volume:
V = (0.1193 mol * 8.314 J/(mol·K) * 298 K) / 790,000 Pa
V ≈ 0.0045 m^3 (rounded to four decimal places)
Therefore, when the pressure is increased to 790 kPa, the volume of the krypton is approximately 0.0045 m^3.