How many oxygen molecules are there in a 33.8 m3 vessel at a temperature of 27 ° C and a pressure of 1.2 MPa?

How many oxygen molecules are there in a 33.8 m3 vessel at a temperature of 27 ° C and a pressure of 1.2 MPa? What is the average energy of the thermal motion of molecules?

To solve the problem, let’s use the formula:
P = n * u ^ 2 * m0 / 3;
Let’s transform:
p = N * k * t / v;
Let’s substitute:
1.2 * 10 ^ 6 = N * 1.38 * 10 ^ -23 * 300 / 33.8;
40.56 * 10 ^ 6 = 414 * 10 ^ -23 * N;
It is important to know that: N = 98 * 10 ^ -17;
m0 = M / Na;
m0 = 16 / 6.23 * 10 ^ 23;
m0 = 2.56 * 10 ^ -23;
Let’s use the formula:
n = N / v;
n = 98 * 10 ^ -17 / 33.8 = 2.90 * 10 ^ -17;
1.2 * 10 ^ 6 = 2.56 * 10 ^ 23 * u ^ 2 * 2.90 * 10 ^ -17 / 3;
3.6 * 10 ^ 6 = 7.424 * 10 ^ 6 * u ^ 2;
0.4849 = u ^ 2;
u = 0.69
Answer: u = 0.69