A 50 liter cylinder contains gas under a pressure of 2 MPa at a temperature of 27 degrees.

A 50 liter cylinder contains gas under a pressure of 2 MPa at a temperature of 27 degrees. What kind of gas is it if its mass is 80 g?

To solve this problem, we use the Mendeleev-Clapeyron equation (it is also the equation of state of an ideal gas), it will allow us to find the molar mass of a gas and, using the periodic table, determine what kind of gas it is.

pV = (m / M) * RT

Now let’s translate all the values ​​into the SI system so as not to get confused with the dimensions !!!

p- pressure (2 MPa) = 2 * 10 ^ 6 Pa = 2,000,000 Pa
V – volume (50l) = 50 dm ^ 3 = 0.050 m ^ 3
R – universal gas constant = 8.314 J / (mol * K)
T – temperature (27 * C) = 27 + 273 = 300 K
m – mass (80 g) = 0.080 kg
M is the molar mass to be found

Let’s find “M”:
2000000 * 0.05 = (0.080 / M) * 8.314 * 300
100000 = (0.080 * 8.314 * 300) / M
M = 0.001995 kg / mol = 1.995 g / mol

Now let’s look at the periodic table, the closest gas is hydrogen (H2) (note that a molecule of 2 atoms)
Answer: the target gas is hydrogen H2