Question

When x molecules are removed from $200$ mg of ${N_2}O$,$2.89 \times {10^{ - 3}}$ moles of ${N_2}O$ are left. x will be

Answer 1

Hint: The number of moles is defined as the ratio of the given mass divided by the molecular mass. The initial number of moles need to find out. The value of x will be the number of molecules corresponding to the number of moles removed by the formula.

Complete step-by-step answer:
 We have been given the mass of nitrous oxide that is two hundred gram. We have been given $200$ mg of nitrous oxide, ${N_2}O$ .
We will have to find the initial number of moles of nitrous oxide. The number of moles is equal to the ratio of given mass by molecular mass
$ \Rightarrow n = \dfrac{m}{M}$
Where n is the number of moles
m is the given mass
M is the molecular mass
So the number of moles of two hundred milligrams of nitrous oxide i.e. $200\;mg$ of ${N_2}O$
The molecular mass of nitrous oxide,${N_2}O$ = $2$ (Atomic mass of nitrogen atom) $ + $ (Atomic mass of oxygen atom)
The molecular mass of nitrous oxide, ${N_2}O$=$2(14) + 16$ = $28 + 16 = 44$ $g\;mo{l^{ - 1}}$
Here initial moles of nitrous oxide,${N_2}O$=$\dfrac{{200 \times {{10}^{ - 3}}}}{{44}} = 4.55 \times {10^{ - 3}}$
Now the number of moles removed will be the difference between the initial moles and the final number of moles.
So moles removed= initial number of moles- final number of moles.
 $ \Rightarrow 4.55 \times {10^{ - 3}} - 2.89 \times {10^{ - 3}}$
 $ \Rightarrow 1.66 \times {10^{ - 3}}$ moles
Further, we know that the number of molecules is equal to the number of moles times Avogadro's number.
Therefore, the number of molecules= $n \times {N_A}$
So the number of molecules $ = $$6.023 \times {10^{23}} \times 1.66 \times {10^{ - 3}}$$ = 9.996 \times {10^{20}}$
We take the approximation of $9.996 \simeq 10$ so the final number of molecules will be as follows
Number of molecules = $10 \times {10^{20}} = {10^{21}}$ molecules

Hence the correct value of x is ${10^{21}}$

Note: We should remember that one mole contains $6.022 \times {10^{23}}$ molecules. The correct approximation should be taken for finding the number of molecules .It is done to match according to the options given in the question.