Molar volume of a gas can be defined as volume of gas occupied by one mole of gas at 1 atm pressure and 273K temperature. If you use ideal gas equation volume of one mole of gas will be 22.4L. which is known as molar volume of gas at STP.

The results of the laws of Boyle and Gas-Lussac can be combined into an expression which represents the relationship between pressure, volume and temperature of a given mass of a gas; such an expression is described as an equation of state.

Suppose the gas is in the initial state with volume, V1, pressure p1and temperature T1. We then change the state of the gas to a volume V2, pressure p2 and temperature T2. Let us carry out this change in two steps.

(i) First, we change the pressure from p1 to p2 keeping the temperature T1 constant. The resultant volume Vr as given by Boyle’s law is

(ii) Next, temperature is changed from T1 to T2, keeping the pressure p2 constant. The final volume V2 as given by Charles law is

or

It follows that no matter how we change the state of the given amount of a gas, the ratio pV/T always remains constant, i.e.

The value of K depends on the amount of gas in the system. Since V is an extensive property (which is mass dependent), its value at constant p and T is proportional to the amount of the gas present in the system. Then K must also be proportional to the amount of gas because p and T are intensive properties (which have no mass dependence). We can express this by writing K = nR, in which n is the amount of gas in a given volume of gas and R is independent of all variables and is, therefore, a universal constant. We thus have the general gas law

pV = nRT

The universal gas constant R = pV/nT. Thus, it has the unit of (pressure volume) divided by (amount of gas temperature). Now the dimensions of pressure and volume are, Pressure = (force/area) = (force/length2) = force length−2

Volume = length3

Thus

Thus, the dimensions of R are energy per mole per kelvin and hence it represents the amount of work (or energy) that can be obtained from one mole of a gas when its temperature is raised by one kelvin.

• Numerical Values of R

i) In liter atmosphere = 0.0821 litre atm deg–1 mole–1 ii) In ergs = 8.314 107 erg deg–1 mole–1

iii) In calories = 1.987 cal deg–1 mole–1 iv) In Joules = 8.314 J deg–1 mole–1

• Use the value of R depending on the units in which value of pressure and volume has been used in ideal gas equation.

**Q. **What mass of ammonia will exert same pressure as 12 g of H2S(g) in the same container under the similar conditions of temperature?

**Ans**: Under identical conditions of T and V, p n

equal moles of ammonia as that of H2S(g) will exert same pressure, when confined in

the same container

Moles of H¬2S = 12/34 = moles of ammonia

Mass of ammonia = (12/34) 17 = 6g

**Q. **4 g of an ideal gas was confined in a 1.0 L flask at 1.0 atm. Increasing temperature of flask by 30^{o}C increases gas pressure by 8%. Determine molar mass of gas.

**Ans:** Let the initial temperature be, TK.

Since, n and V are constants P_{1}/T_{1}= P_{2}/T_{2}

Since pV = nRT and n = w/M

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