Question

A mixture of $MgO$ and $Mg$ weighing $10g$ is treated with excess of dilute $HCl$ . Then $2.24litre$ of ${H_2}$ gas was liberated under STP conditions. The mass of $MgO$ present in the sample is:
A. $2.4g$
B. $7.6g$
C. $8g$
D. $2g$

Answer 1

Hint:STP refers to the standard condition for temperature and pressure. It is defined at the temperature of $273.15K$ and pressure of exactly $1atm$ . At these two conditions of temperature and pressure the volume of one mole of substance is always $22.4litre$ . Atomic mass of magnesium is $24$ .

Complete step by step answer:
According to the question, the reaction will be followed as:
$Mg + 2HCl \to MgC{l_2} + {H_2}$
As we know that at STP one mole of magnesium will give $22.4litre$ of ${H_2}$ gas.
But according to the question,
The weight of magnesium used is giving $2.24litre$ of ${H_2}$ gas at STP will be calculated as:
 $\
   \Rightarrow \left( {\dfrac{{2.24 \times 24}}{{22.4}}} \right)g \\
   \Rightarrow 2.4g \\
\ $
Now, the total weight of magnesium oxide and magnesium is $10g$
Mass of magnesium = $2.4g$
So, weight of magnesium oxide will be :
$\
   \Rightarrow (10 - 2.4)g \\
   \Rightarrow 7.6g \\
\ $
The mass of $MgO$ is $7.6g$ .

Hence, option B is correct.

Note:
STP, which is standard temperature and pressure condition, is a reference which is used for the molar volume of an ideal gas. Hydrogen and helium are two gases which show positive deviation from ideal behavior at all pressure and $273K$ temperature. As are the lightest gases known. So, Their molecules have very small masses. So, the attractive forces between the molecules of these two gases are extensively small. So $a/{V^2}$ is negligible even at ordinary temperatures. Thus $PV > RT$ . Thus the Vander Waals equation describes the observed behaviour of real gases (quantitatively) and so it is an improvement over the ideal gas equation. At all temperatures, if the pressure is extremely high then there will be a positive deviation because of the size of the molecules.The causes of deviations from ideal behaviour is due to the kinetic theory of gases. Kinetic theory of gas assumes that the volume occupied by gas molecules is very small as compared to the volume occupied by the gas and the forces of attraction between gas molecules are negligible.