Question

The mass of hydrogen at STP, that is present in a vessel which can hold 4 grams of oxygen under similar conditions, is:
A. 1 gm
B. 0.5 gm
C. 0.25 gm
D. 0.125 gm

Answer 1

Hint: According to Avogadro's law, equal volume of all gases under similar conditions of temperature and pressure contain equal numbers of molecules. At STP, as temperature and pressure are constant only the number of moles of gas are needed to calculate mass and volume.

Complete step-by-step answer:
If some mass of hydrogen at STP is present in a vessel that can hold 4 grams of oxygen under the same conditions is possible due to Avogadro's law which states that equal volumes of all gases under similar conditions of temperature and pressure contain the same number of molecules.
The formula used for the same is:
 \[number\,of\,molecules = \dfrac{{given{\text{ }}weight \times {N_A}}}{{molar\,weight}}\]
Where, gram atomic weight is the mass of Avogadro number of atoms of that element in grams. We are given the weight of oxygen as 4 grams and we know that the gram molecular weight of oxygen is 16gms.
 Number of molecules of hydrogen will be equal to the number of molecules of oxygen.
\[\dfrac{{{{(given{\text{ }}weight)}_{hydrogen}} \times {N_A}}}{{{{(molar\,weight)}_{hydrogen}}}} = \dfrac{{{{(given{\text{ }}weight)}_{oxygen}} \times {N_A}}}{{{{(molar\,weight)}_{oxygen}}}}\]
Putting the values in the formula, we get-
 \[\dfrac{{{{(given\,\,weight)}_{hydrogen}}}}{2} = \dfrac{4}{{32}}\]
\[\therefore \] \[weight\,of\,hydrogen = 0.25gms\]
From this, we conclude that 0.25gms of hydrogen at STP is present in a vessel which can hold 4 grams of oxygen under similar conditions.

Hence, the correct option is (C).

Note: There is an alternative method too. We can calculate moles of oxygen present in the vessel by dividing given mass by molar mass that will come out to be 0.125 moles. This is equal to the number of moles of hydrogen having molar mass 2gms, as per Avogadro’s law. Therefore, calculated mass will be multiplication of 0.125moles and 2gms, i.e. 0.25gms.