Calculate each of the following quantities for an ideal gas (a) the volume Free 68A

by
with no comment
Chemistry

Calculate each of the following quantities for an ideal gas: (a) the volume of the gas, in liters, if 1.50 mol has a pressure of 1.25 atm at a temperature of -6 °C; (b) the absolute temperature of the gas at which 3.33 * 10-3 mol occupies 478 mL at 750 torr; (c) the pressure, in atmospheres, if 0.00245 mol occupies 413 mL at 138 °C; (d) the quantity of gas, in moles, if 126.5 L at 54 °C has a pressure of 11.25 kPa.

Answer

Ideal Gas Law Problems Solved | Volume, Temperature, Pressure & Moles

Ideal Gas Law Problem Solving Using PV = nRT

The Ideal Gas Law is a fundamental equation in chemistry used to relate the pressure, volume, temperature, and amount of a gas. It is expressed as:

PV = nRT

Where:

  • P = pressure (atm)
  • V = volume (liters)
  • n = number of moles (mol)
  • R = ideal gas constant = 0.0821 L·atm/mol·K
  • T = temperature (Kelvin)

🔹 Part A: Calculate Volume

Given:

  • n = 1.50 mol
  • P = 1.25 atm
  • T = -6°C = 267 K

Step-by-step:

Use the formula:
V = (nRT) / P

V = (1.50 mol × 0.0821 L·atm/mol·K × 267 K) / 1.25 atm
V = (32.84805) / 1.25 = 26.28 L
✅ The volume of the gas is 26.28 liters

🔹 Part B: Calculate Temperature

Given:

  • n = 3.33 × 10⁻³ mol
  • V = 478 mL = 0.478 L
  • P = 750 torr = 0.987 atm

Step-by-step:

Use the formula:
T = (PV) / (nR)

T = (0.987 atm × 0.478 L) / (3.33 × 10⁻³ mol × 0.0821)
T = (0.471186) / (0.000273393) ≈ 1723.83 K
✅ The absolute temperature of the gas is 1724 K

🔹 Part C: Calculate Pressure

Given:

  • n = 0.00245 mol
  • V = 413 mL = 0.413 L
  • T = 138°C = 411 K

Step-by-step:

Use the formula:
P = (nRT) / V

P = (0.00245 mol × 0.0821 × 411 K) / 0.413 L
P = (0.082718) / 0.413 ≈ 0.2003 atm
✅ The pressure is 0.200 atm

🔹 Part D: Calculate Number of Moles

Given:

  • V = 126.5 L
  • T = 54°C = 327 K
  • P = 11.25 kPa = 0.111 atm

Step-by-step:

Use the formula:
n = (PV) / (RT)

n = (0.111 atm × 126.5 L) / (0.0821 × 327)
n = (14.0415) / (26.8587) ≈ 0.5229 mol
✅ The quantity of gas is 0.523 mol

📚 Final Notes & Tips

  • Always convert temperature to Kelvin: K = °C + 273
  • Convert mL to L by dividing by 1000
  • Convert torr to atm using: 1 atm = 760 torr
  • Convert kPa to atm using: 1 atm = 101.325 kPa
  • Use the ideal gas constant R = 0.0821 L·atm/mol·K

🔍 Why This Matters

The Ideal Gas Law gives us a mathematical model for understanding the relationships between pressure, volume, temperature, and the amount of gas. It’s essential in chemical engineering, thermodynamics, environmental science, and even meteorology.

Whether you’re calculating how much air a balloon can hold, analyzing gases in a lab, or solving standardized test problems, mastering PV = nRT will open many doors in physical science.

Add a Comment

Your email address will not be published. Required fields are marked *