Question

vacuum line is lowered to a pressure of 1.3kpa and 77 k find the number of moles per mm3. Assume that R= 8.31 JK-1 mol-1

Answer 1

The number of moles per mm³=2.032 x 10⁻⁹

Further explanation

In general, the gas equation can be written  

$\large {\boxed {\bold {PV = nRT}}}$

where  

P = pressure, atm , N/m²

V = volume, liter  

n = number of moles  

R = gas constant = 0.082 l.atm / mol K (P= atm, v= liter),or 8.314 J/mol K (P=Pa or N/m2, v= m³)

T = temperature, Kelvin  

P=1.3 kPa=1.3.10³ N/m²

T = 77 K

R = 8.31 J/mol.K

$\tt PV=nRT\\\\\dfrac{n}{V}=\dfrac{P}{RT}\\\\\dfrac{mol}{m^3}=\dfrac{1.3\times 10^3}{8.31\times 77}\\\\\dfrac{mol}{m^3}=2.032\\\\2.032\dfrac{mol}{m^3}\times \dfrac{m^3}{10^9cm^3}=2.032\times 10^{-9}\dfrac{mol}{cm^3}$