# The mean square velocity of gas molecules under normal conditions is 500 m / s.

The mean square velocity of gas molecules under normal conditions is 500 m / s. How many molecules are there in 10 g of this gas?

Let’s start with a short entry given. We immediately translate all the specified values into the SI system:

v = 500 m / s;

m = 0.01 kg;

T = 273 K.

Find:

N -?

Let’s apply a number of formulas to solve. Let’s start by finding the number of molecules:

N = m / m0;

E = (m0 * v ^ 2) / 2;

E = 3 / 2kT.

We equate the last two formulas and the expression from the equality m0:

(m0 * v ^ 2) / 2 = 3 / 2kT.

m0 = 3kT / v ^ 2.

We substitute the values into the formula and perform the calculations:

m0 = (3 * 1.38 * 10 ^ -23 * 273) / 500 ^ 2 = 0.00452 * 10 ^ -23 kg.

N = 0.01 / 0.00452 * 10 ^ -23 = 2 * 10 ^ 23.

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