A 334-mL cylinder for use in chemistry lectures contains 5.225 g of helium at 23 °C. How many grams of helium must be released to reduce the pressure to 7.60 MPa assuming ideal gas behavior?

Verified step by step guidance

1. Identify the initial conditions: initial volume (V) = 334 mL, initial mass of helium (m) = 5.225 g, initial temperature (T) = 23 °C, and initial pressure (P) is unknown.
2. Convert the temperature from Celsius to Kelvin using the formula: T(K) = T(°C) + 273.15.
3. Use the ideal gas law, PV = nRT, to find the initial pressure. First, calculate the number of moles (n) of helium using the molar mass of helium (4.00 g/mol).
4. Rearrange the ideal gas law to solve for the initial pressure: P = (nRT)/V. Use R = 8.314 J/(mol·K) and convert volume to liters.
5. Determine the final number of moles needed to achieve the desired pressure of 7.60 MPa using the ideal gas law again, and calculate the mass of helium to be released by finding the difference in moles and converting it to grams.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law assumes that gas particles do not interact and occupy no volume, making it a useful approximation for many gases under standard conditions.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For helium, the molar mass is approximately 4.00 g/mol. Understanding molar mass is essential for converting between grams and moles, which is necessary for applying the Ideal Gas Law and determining how many grams of helium must be released to achieve a desired pressure.

Pressure Units

Pressure is a measure of force applied per unit area and can be expressed in various units, including pascals (Pa), atmospheres (atm), and megapascals (MPa). In this question, the pressure is given in megapascals, where 1 MPa equals 1,000,000 pascals. Understanding how to convert and manipulate these units is crucial for solving problems involving gas behavior and ensuring that calculations are consistent.