Ideal Gas Law: Calculating Volume of Ideal Gas

How can we calculate the volume of 4.37 moles of an ideal gas at 29.5°C and 1.00 atm?

Final answer: The volume of 4.37 moles of an ideal gas can be calculated using the ideal gas law equation 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.

To calculate the volume of the gas, we need to convert the temperature from Celsius to Kelvin by adding 273.15. So, the temperature becomes 29.5 + 273.15 = 302.65 K.

When dealing with ideal gases, the ideal gas law equation PV = nRT is a fundamental concept to understand. This equation relates the pressure (P), volume (V), number of moles (n), ideal gas constant (R), and temperature (T) of an ideal gas. By manipulating this equation, we can solve for any of the variables as needed in a given scenario.

In the provided question, we are asked to determine the volume of 4.37 moles of an ideal gas at a pressure of 1.00 atm and a temperature of 29.5°C. To solve this, we first convert the temperature from Celsius to Kelvin by adding 273.15, resulting in 302.65 K. With the known values of n = 4.37 moles, P = 1.00 atm, R = 0.0821 atm L/mol K (ideal gas constant), and T = 302.65 K, we can plug these values into the ideal gas law equation.

By rearranging the equation to solve for volume (V), we get V = (nRT) / P. Substituting the values, we calculate the volume as V = (4.37 mol * 0.0821 atm L/mol K * 302.65 K) / 1.00 atm = 107.394 L. Therefore, the volume of 4.37 moles of the ideal gas at 29.5°C and 1.00 atm is 107.394 liters.

Understanding and applying the ideal gas law in calculations like these is crucial in the field of chemistry and helps us determine various properties of gases under different conditions. It allows us to make predictions and analyze the behavior of gases, providing valuable insights into their properties and interactions.