Solveeit Logo
Login

Question

Question: When x molecules are removed from \(200\) mg of \({N_2}O\),\(2.89 \times {10^{ - 3}}\) moles of \({N...

When x molecules are removed from 200200 mg of N2O{N_2}O,2.89×10−32.89 \times {10^{ - 3}} moles of N2O{N_2}O are left. x will be

Explanation

Solution

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 200200 mg of nitrous oxide, N2O{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
⇒n=mM\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  mg200\;mg of N2O{N_2}O
The molecular mass of nitrous oxide,N2O{N_2}O = 22 (Atomic mass of nitrogen atom) ++ (Atomic mass of oxygen atom)
The molecular mass of nitrous oxide, N2O{N_2}O=2(14)+162(14) + 16 = 28+16=4428 + 16 = 44 g  mol−1g\;mo{l^{ - 1}}
Here initial moles of nitrous oxide,N2O{N_2}O=200×10−344=4.55×10−3\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.
⇒4.55×10−3−2.89×10−3\Rightarrow 4.55 \times {10^{ - 3}} - 2.89 \times {10^{ - 3}}
⇒1.66×10−3\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×NAn \times {N_A}
So the number of molecules == 6.023×1023×1.66×10−36.023 \times {10^{23}} \times 1.66 \times {10^{ - 3}} =9.996×1020 = 9.996 \times {10^{20}}
We take the approximation of 9.996≃109.996 \simeq 10 so the final number of molecules will be as follows
Number of molecules = 10×1020=102110 \times {10^{20}} = {10^{21}} molecules

Hence the correct value of x is 1021{10^{21}}

Note: We should remember that one mole contains 6.022×10236.022 \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.