At what temperature T does a gas with a volume of V = 1 cm3 contain N = 1 * 10 ^ 19 molecules

At what temperature T does a gas with a volume of V = 1 cm3 contain N = 1 * 10 ^ 19 molecules, if its pressure is p = 1 * 10 ^ 4 Pa?

Data: V (volume of taken gas) = 1 cm3 (in SI V = 1 * 10 ^ -6 m3); N (number of molecules) = 1 * 1019 molecules; P (pressure) = 1 * 10 ^ 4 Pa.

Constants: Na (Avogadro’s number) = 6.02 * 10 ^ 23 mol-1; R (universal gas constant) = 8.31 J / (mol * K).

To determine the temperature of the taken gas, we use the equation of state for an ideal gas: P * V = m / M * R * T = N / Na * R * T, whence T = P * V * Na / (N * R).

Calculation: T = 1 * 10 ^ 4 * 1 * 10 ^ -6 * 6.0 ^ 2 * 10 ^ 23 / (1 * 10 ^ 19 * 8.31) = 72.44 K (-200.56 ºС) …