Question

(i) If $150$ cc of gas A contains X molecules, how many molecules of gas B will be present in$75$ cc of B? The gas A and B are under the same conditions of temperature and pressure.
(ii) Name the law on which the given problem is based.

Answer 1

Hint:To answer this question we should know the ideal gas equation. According to which product of pressure and volume is equal to the product of the number of moles, gas constant, and temperature. We will write the ideal gas equation for both of the given gases. Then by comparing both equations we will determine the mole of B gas.

Complete step-by-step solution:(i)The formula of the ideal gas is as follows:
${\text{pV = nRT}}$
${\text{p}}$is the pressure
V is the volume
${\text{n}}$ is the number of moles of ideal gas
R is the gas constant
T is the temperature
It is given that the gas A and B are under the same conditions of temperature and pressure and R is already constant.
So, volume is directly proportional to the number of moles.
We can write the above equation for gas A and B as,
${{\text{V}}_{\text{A}}}{\text{ = }}{{\text{n}}_{\text{A}}}$…..$(1)$
${{\text{V}}_{\text{B}}}{\text{ = }}{{\text{n}}_{\text{B}}}$…..$(2)$
We dividing the equation $(1)$ with $(2)$ we get,
\[\frac{{{{\text{V}}_{\text{A}}}}}{{{{\text{V}}_{\text{B}}}}}{\text{ = }}\frac{{{{\text{n}}_{\text{A}}}}}{{{{\text{n}}_{\text{B}}}}}\]
On substituting $150$ cc for volume of gas A, X for mole of gas A, $75$ cc for volume of gas B,
\[\frac{{{\text{150}}}}{{{\text{75}}}}{\text{ = }}\frac{{\text{X}}}{{{{\text{n}}_{\text{B}}}}}\]
\[{{\text{n}}_{\text{B}}}{\text{ = }}\frac{{{\text{75X}}}}{{{\text{150}}}}\]
\[{{\text{n}}_{\text{B}}}{\text{ = }}\frac{{\text{X}}}{2}\]
So, the molecules of gas B will be present in$75$ cc of B is X/\[2\].
Therefore, X/\[2\] is the correct answer.
(ii) We use the following equation to solve the part (i).
${\text{pV = nRT}}$
This equation is known as the ideal gas equation and the law is the ideal gas law.
Therefore, the law on which the given problem is based is Avogadro law which is ideal gas law.

Note:Here, we have to compare two different gases in the same condition, so we used the ideal gas law. If we have to compare the same gas at different conditions then we use the combined gas law. According to this law, if an ideal gas is present at a condition of temperature, pressure, and volume, and any one or two parameters of temperature, pressure, or volume get changed then we can determine the third parameter by putting the initial conditions of temperature pressure and volume equal to the final condition of temperature, pressure, and volume. The relation between temperature pressure and volume of an ideal gas according to combined gas law is as follows:
$\frac{{{{\text{p}}_{\text{1}}}{{\text{V}}_{\text{1}}}}}{{{{\text{T}}_{\text{1}}}}}\, = \,\frac{{{{\text{p}}_2}{{\text{V}}_2}}}{{{{\text{T}}_2}}}$