Final answer:
To determine the temperature at which helium occupies the given volume and pressure, we use the Ideal Gas Law equation PV = nRT. After calculating the number of moles of helium and converting units as needed, we solve for the temperature in Kelvin and then convert it to Celsius.
Step-by-step explanation:
To find the temperature at which 5.43 g of helium occupies a volume of 7.23 L at a pressure of 1.59 atm, we can use the Ideal Gas Law, which is stated as PV = nRT. Here, P represents pressure, V is volume, n is the number of moles, R is the Ideal Gas Constant, and T is temperature in Kelvin. We will first need to convert the mass of helium into moles using its molar mass (approximately 4.00 g/mol for helium) and then solve for the temperature.
- Calculate the number of moles of helium: n = mass / molar mass = 5.43 g / 4.00 g/mol = 1.3575 moles.
- Convert the pressure from atm to Pa as the value of R in these units is commonly known: 1 atm = 101325 Pa, so 1.59 atm = 1.59 x 101325 Pa.
- Use the Ideal Gas Law and solve for T (in K): (1.59 atm x 7.23 L) = (1.3575 mol x R x T). To get T in Celsius, subtract 273.15 from the T in Kelvin.
Plug in the values and solve for the temperature T. Remember to convert your answer from Kelvin to Celsius to match the units asked in the question.