Question

How many molecules are likely to be present in a cubic centimeter of volume if the pressure is 20 mm of Hg and the temperature is 27°C?
1. 6.4 x 10¹⁷
2. 6.4 x 10²³
3. 4.8 x 10¹⁵
4. 4.8 x 10²¹

Answer 1

Correct Answer - Option 1 : 6.4 x 10¹⁷

CONCEPT:

BEHAVIOUR OF GASES:

• In gases, the molecules are far apart and mutual interactions amongst the molecules are negligible except when they collide.
• At low pressures and high temperatures (much above the temps at which gases liquefy or solidify), the gases follow a simple relation

⇒ PV = KT    ------ (1)

Where P = pressure, V = volume, and T = temperature of a given mass of gas. K = constant that varies with the volume of the gas or with a number of atoms/molecules of the gas in the sample.

We can write, K = NkB      ------ (2)

Where N = number of molecules and kb = Boltzmann constant = 1.38 × 10-23 JK-1, which is the same for every gas.

Combining equation 1 and 2, we get

\(⇒ PV=Nk_BT\)

EXPLANATION:

Given - Volume (V) = 1 cm³ = 10^-6 m³, Pressure (P) =  20 mm of Hg = 2666.45 Pa, and temperature (T) = 27°C = 300 K

• The number of molecules present in a cubic centimeter of the volume is 

\(\Rightarrow N=\frac{PV}{k_BT}\)

\(\Rightarrow N=\frac{2666.45\times 10^{-6}}{1.38\times 10^{-23}\times 300}=6.4 \times 10^{17}\)