Question

Find the approx no of molecules contained in a vessel of volume 7 litres at 0°c at 1.3 ×10^5 pascal

Answer 1

given, pressure , P= 1.3 × 10^5 Pascal = 1.283 atm
volume, V = 7 litres
temperature, T = 0°C = 273K

we know from ideal gas law,

PV = nRT

n = RT/PV

= 0.082 × 273/(1.283 × 7) [ R = 0.082 L.atm/mol/k]

= 2.49

hence, number of mole = 2.49

so, number of molecules = mole × 6.023 × 10²³

= 2.49 × 6.023 × 10²³

= 14.99 × 10²³ ≈ 1.5 × 10²⁴

hence, number of molecules = 1.5 × 10²⁴

Answer 2

PV=nRT

n=PV/RT

1 ATM=101325 Pascal

So,1.3x10^5=(k)x101325

Therefore,

k=1300000/101325=1.28

So,P=1.28

n=PV/RT

=1.28x7/0.0821x273(0°C)

=0.4 moles

Molecules=(moles)x(Avagadros number)

=(0.4)x(6.022x10^²³)

=2.4x10^²³