IDEA GAS EQUATION at a glance

 IDEAL GAS EQUATION

The ideal gas equation is:

                                    PV = nRT

Where:

• P = pressure of the gas

• V = volume of the gas

• n = number of moles of the gas

• R = universal gas constant

• T = absolute temperature (in Kelvin)

Value of R 

•  R = 8.31{J mol-1K-1

📌 Important tip:
Temperature must always be converted to Kelvin (K) using

T(K) = t(0C) + 273

This equation states that for an ideal gas PV/T is a constant.

That is, PV = R 
               T

(R = molar gas constant)

             

             PV = RT

That is, for n mole of a gas, the equation becomes

             PV = nRT

 

CALCULATIONS

1.  Calculate the number of moles present in a certain mass of gas occupying 6.5dm³ at     3atm and 15^oC (R = 0.082atmdm³K^-1mol^-1)

    Solution:

    V = 6.5dm³, P = 3atm, T = 15^oC = (15 + 273)K = 288K, n =?

    Using PV = nRT

           n = PV = 3atm x 6.5dm³= 0.8257

                RT    0.082atmdm³K^-1mol^-1 x 288K

    Number of moles = 0.83 mole

Finding the volume of a gas

2. Calculate the volume occupied by 2 moles of an ideal gas at a pressure of 1.0 × 10⁵ Pa and a temperature of 27°C.

R = 8.31J mol^-1,/sup>K-1

Solution:
Convert temperature to Kelvin:

T = 27 + 273 = 300K

Use the formula:

PV = nRT

Make V the subject:

V =          nRT

                   P

Substitute values:

         V =   2 x 8.31 x 300
                    1.0 x 10⁵

     V =        4986
                 100000

V = 0.0499 m³

Answer:
V = 4.99 x10^-2m³

Finding pressure

Question:
3. A gas occupies a volume of 0.02 m³ at 300 K and contains 1 mole of gas. Calculate its pressure.

Solution:

           PV = nRT

Make P the subject:

               P = nRT
                      V

Substitute:

P =          1 x 8.31 x 300
                       0.02

P =       2493
             0.02

P = 124650 Pa

Answer:
            P = 1.25 x 10⁵ Pa

Finding number of moles

Question:
4. Calculate the number of moles of a gas that occupies 0.01 m³ at 27°C and 1.0 × 10⁵ Pa.

Solution:
Convert temperature:

T = 27 + 273 = 300K

Use:

         n =    PV
                  RT

Substitute:

             n = 1.0 x 10⁵ x 0.01
                      8.31 x 300

                n = 1000
                       2493

               n = 0.40 mol

Answer:
                    n = 0.40 mol

Converting cm³ to m³

Question:
5.  A gas occupies 500 cm³ at 27°C and 1.0 × 10⁵ Pa. Find the number of moles.

Solution:
Convert volume:
500 cm³ = 5.0 x 10^-4 x m³

Convert temperature:

T = 300K

n =   PV
        RT

n = 1.0 x 10⁵ x 5.0 x 10^-4
          8.31 x 300

       n =    50
              2493

n = 0.020 mol

Answer:
                n = 0.02 mol

🔑 Important EXAM TIPS

• Always convert °C to K

• Convert cm³ to m³

• Write formula first

• Show substitutions clearly

OBJECTIVE QUESTION

1. The ideal gas equation is written as
   A. PV = RT 
   B. P = VRT 
   C. PV = nRT 
   D.  V = nRP 

2. In the ideal gas equation PV = nRT the symbol n represents
   A. number of molecules
   B. number of particles
   C. number of moles
   D. molar volume

3. Which of the following is the correct unit of the gas constant R?
   A. J K⁻¹
   B. J mol⁻¹
   C. J mol⁻¹ K⁻¹
   D. Pa m³ mol⁻¹

4. In gas calculations, temperature must be expressed in
   A. Celsius
   B. Fahrenheit
   C. Kelvin
   D. Centigrade

5. A gas occupies a volume of 0.02 m³ at 300 K and 1 mole. Calculate the pressure.
   A. ( 4.2 x10^4 ) Pa
   B. ( 8.3 x 10^4 ) Pa
   C. ( 1.25 x10^5 ) Pa
   D. ( 2.49 x 10^5 ) Pa

6. Which of the following is an assumption of an ideal gas?
   A. Gas molecules attract one another
   B. Gas molecules occupy large volumes
   C. Gas molecules are in constant random motion
   D. Gas molecules move in one direction

7. If the temperature of a gas increases while pressure remains constant, the volume will
   A. decrease
   B. remain constant
   C. increase
   D. become zero

8. Which law is combined with Boyle’s and Charles’ laws to give the ideal gas equation?
   A. Dalton’s law
   B. Avogadro’s law
   C. Graham’s law
   D. Faraday’s law

9. The volume of a gas is 500 cm³ at STP. What is this volume in m³?
   A.  5.0 x 10^-2
   B. 5.0 x 10^-3
   C. 5.0  x 10^-4
   D.  5.0 x 10^-5

10. Real gases behave most like ideal gases at
    A. low temperature and high pressure
    B. high temperature and high pressure
    C. low temperature and low pressure
    D. high temperature and low pressure