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Question: The molecular weight of \[{{\text{O}}_{\text{2}}}\] and \[\text{S}{{\text{O}}_{\text{2}}}\] are 32 a...

The molecular weight of O2{{\text{O}}_{\text{2}}} and SO2\text{S}{{\text{O}}_{\text{2}}} are 32 and 64 respectively. If one litre of O2{{\text{O}}_{\text{2}}} at 15 degree Celsius and 759mm pressure contains N molecules, the number of molecules in two litre of SO2\text{S}{{\text{O}}_{\text{2}}} under the same conditions of temperature is –
a.) N/2
b.) N
c.) 2N
d.) 4N

Explanation

Solution

Hint: To solve the given question, use the ideal gas equation. Then relate volume with the number of moles using Avogadro’s Law.

Complete step by step solution:
Let us define Avogadro’s law first.
Avogadro’s law states that “equal volumes of gases at the same temperature and pressure contain equal numbers of molecules”.
Therefore, V ∝\propto n,
So, V1V2=n1n2\dfrac{{{\text{V}}_{\text{1}}}}{{{\text{V}}_{\text{2}}}}=\dfrac{{{\text{n}}_{\text{1}}}}{{{\text{n}}_{\text{2}}}}
Where ‘V’ is the volume and ‘n’ is the number of moles.
According to the question, both O2{{\text{O}}_{\text{2}}}and SO2\text{S}{{\text{O}}_{\text{2}}}are at the same atmospheric conditions, i.e. at 15 degree Celsius and 759mm pressure.
As we know, V1V2=n1n2\dfrac{{{\text{V}}_{\text{1}}}}{{{\text{V}}_{\text{2}}}}=\dfrac{{{\text{n}}_{\text{1}}}}{{{\text{n}}_{\text{2}}}}
Let -
V1{{\text{V}}_{\text{1}}} = volume of Oxygen
V2{{\text{V}}_{\text{2}}}= volume of Sulphur dioxide
n1{{\text{n}}_{\text{1}}}= moles of Oxygen
n2{{\text{n}}_{\text{2}}}= volume of Sulphur dioxide
Putting the values in Avogadro’s equation, we can find the volume of Sulphur dioxide.
1N=2n2\dfrac{\text{1}}{\text{N}}\text{=}\dfrac{\text{2}}{{{\text{n}}_{\text{2}}}}
Therefore, n2{{\text{n}}_{\text{2}}}=2N
Hence, the answer is – option (c) – the number of molecules in two litre of SO2\text{S}{{\text{O}}_{\text{2}}} under the same conditions of temperature is 2N.

Note: The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas, which combines three laws, namely – Boyle’s Law (Temperature - Volume relationship), Charles’s Law (Pressure – Temperature relationship) and Avogadro’s Law (Volume – amount relationship). In order to solve such types of questions, just remember PV = nRT.