Question

Nitrogen gas is introduced into a large deflated plastic bag. no gas is allowed to escape, but as more and more nitrogen is added, the bag inflates to accommodate it. the pressure of the gas within the bag remains at 1.00 atm and its temperature remains at room temperature (20.0?c). how many moles n have been introduced into the bag by the time its volume reaches 22.4 l

Answer 1

By using the ideal gas law and given constants for pressure, temperature, and volume, it is determined that the number of moles of nitrogen gas added to the bag to reach a volume of 22.4 L at 1.00 atm pressure and 20.0°C is 1 mole.

Step-by-step explanation:

The question posed relates to the ideal gas law, which states that the relationship between the pressure, volume, temperature, and amount of a gas can be described by the formula 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. Given the conditions of pressure remaining at 1.00 atm, temperature constant at 20.0°C which equals 293.15 K (since you add 273.15 to convert Celsius to Kelvin), and a final volume of 22.4 L, we apply the ideal gas law to find the number of moles of nitrogen gas.

First, we will need to rearrange the ideal gas law to solve for n: n = PV/RT. Using the values provided, we have: n = (1.00 atm × 22.4 L) / (0.0821 L.atm.mol⁻¹.K⁻¹ × 293.15 K). Calculating this, we find the number of moles of nitrogen gas is 1 mole.

Answer 2

Use the ideal gas equation: pV = nRT

=> n = RT / pV

R = 0.0821 atm*l / K*mol
T = 20 + 273.15 = 293.15 K
p = 1 atm
V = 22.4 l

=> n = 0.0821 atm*l / K*mol * 293.15K / (1atm * 22.4 l) = 1.07 mole

Answer: 1.07 mole