Question

A sample of 6.50 mol of gas in a 5.00 L container is at 65.0 °C.

What is the pressure of the gas?

Answer 1

Using the Ideal Gas Law, the pressure of 6.50 mol of gas in a 5.00 L container at 65.0 °C is calculated to be 43.1 atm. This involves converting temperature to Kelvin and using the ideal gas constant in the appropriate units.

Step-by-step explanation:

To calculate the pressure of a gas, we use the Ideal Gas Law, which is represented by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin. In this scenario, we are given the volume (5.00 L), number of moles (6.50 mol), and the temperature (65.0 °C, which is 338.15 K after conversion). The ideal gas constant, R, has a value of 0.0821 L·atm/(mol·K) when pressure is measured in atmospheres.

Using the Ideal Gas Law, the calculation is as follows:

P = nRT/V

P = (6.50 mol) * (0.0821 L·atm/(mol·K) * (338.15 K)) / (5.00 L)

P = 43.11375 atm

The pressure of the gas in the container is 43.1 atm (rounded to three significant figures).

Answer 2

The gas in a 5.00 L container has a pressure of 17.55 atm.

To figure this out, we use the ideal gas law, which links pressure, temperature, volume, and the number of gas molecules. In this case, with 6.50 mol of gas at 65.0 °C, we follow these steps:

Convert the temperature to Kelvin (65.0 °C + 273.15 = 338.15 K).

Apply the ideal gas law: Pressure = (number of moles * ideal gas constant * temperature) / volume. The ideal gas constant is 0.0821 L·atm/(mol·K).

Substitute the values and calculate: Pressure ≈ (6.50 * 0.0821 * 338.15) / 5.00 ≈ 17.55 atm.

So, the gas pressure in the 5.00 L container, with 6.50 mol of gas at 65.0 °C, is about 17.55 atm.