Question

1.0g of magnesium is burnt with 0.56g ${{\text{O}}_2}$ in a closed vessel. Which reactant is left in excess and how much? (Atomic Weight Mg = 24, O = 16).
$
  {\text{A}}{\text{. Mg, 0}}{\text{.16g}} \\
  {\text{B}}{\text{. }}{{\text{O}}_2},{\text{ 0}}{\text{.16g}} \\
  {\text{C}}{\text{. Mg, 0}}{\text{.44g}} \\
  {\text{D}}{\text{. }}{{\text{O}}_2},{\text{ 0}}{\text{.28g}} \\
$

Answer 1

Hint: To find out the excess, we write down the chemical reaction that takes place when magnesium is burnt with oxygen in a closed vessel. We calculate the number of moles of each reactant is required to obtain the product. We use this relation to find the excess.

Complete step by step answer:
Given Data, 1.0g of magnesium is burnt with 0.56g ${{\text{O}}_2}$

We know, the balanced chemical reaction of the above phenomena is as follows:
${\text{Mg + }}\dfrac{1}{2}{{\text{O}}_2} \to {\text{MgO}}$.

We calculate the number of moles of each of the reactants is required, it is given by the formula
Number of moles of a substance =$\dfrac{{{\text{Mass given}}}}{{{\text{Relative formula mass}}}}$.
The formula mass of Mg and${{\text{O}}_2}$ are 24 and 32 moles respectively as per the chemical properties of magnesium and oxygen.
Hence, the number of moles of Mg and ${{\text{O}}_2}$are $\dfrac{{1.0}}{{24}}$and$\dfrac{{0.56}}{{32}}$, i.e. $\dfrac{{0.5}}{{12}}$and $\dfrac{{0.07}}{4}$respectively.

Let us assume ‘x’ moles of Mg is used up to form MgO, i.e. from the balanced equation, x moles of Magnesium is reacted with $\dfrac{{\text{x}}}{2}$moles of Oxygen to form x moles of Magnesium Oxide.
Hence after the reaction is over, the remaining amount of Magnesium Mg is $\dfrac{{0.5}}{{12}} - {\text{x}}$moles and the remaining amount of oxygen is $\dfrac{{0.07}}{4} - \dfrac{{\text{x}}}{2}$moles.
But in this chemical reaction, oxygen is the limiting reagent, i.e. the reaction goes on until oxygen is available. The reaction only ends after all the oxygen available is over.
Hence the number of moles of left over oxygen must be equal to zero, $\dfrac{{0.07}}{4} - \dfrac{{\text{x}}}{2} = 0$
$ \Rightarrow {\text{x = }}\dfrac{{0.07}}{2}$

Therefore the number of moles of magnesium left over is $\dfrac{{0.5}}{{12}} - {\text{x}}$
$ \Rightarrow \dfrac{{0.5}}{{12}} - \dfrac{{0.07}}{2} = \dfrac{{1 - 0.07 \times 12}}{{24}}{\text{moles}}$
$ \Rightarrow \dfrac{{0.16}}{{24}}{\text{moles}}$

Hence the mass of magnesium leftover = 0.16g
Thus, when 1.0 g of magnesium is burnt with 0.56 g ${{\text{O}}_2}$​ in a closed vessel, 0.16 g magnesium is left in excess.
So, the correct answer is “Option A”.

Note: In order to answer this type of questions the key is to know the balanced chemical reaction of the process given, i.e. magnesium burning in presence of oxygen. It is important to only consider a balanced chemical equation as it represents the number of moles of each of the components.
According to the law of conservation of mass, when a chemical reaction occurs, the mass of the products should be equal to the mass of the reactants. A balanced chemical equation occurs when the number of the atoms involved in the reactants side is equal to the number of atoms in the products side.
The mole is the unit of measurement for the amount of substance in the International System of Units. A mole of a substance or a mole of particles is defined as exactly $6.02214076{\text{ }} \times {\text{ 1}}{{\text{0}}^{23}}$ particles, which may be atoms, molecules, ions, or electrons.