Question
What is the mass of carbon dioxide which contains the same number of molecules as are contained in $$40\,g$$ of oxygen ?
A.
40$$\,g$$
B.
55$$\,g$$
C.
32$$\,g$$
D.
44$$\,g$$
Answer :
55$$\,g$$
Solution :
$${\text{Molar mass of}}\,\,{O_2} = 32\,\,g\,mo{l^{ - 1}}$$
$$32\,\,g\,\,{\text{of}}\,\,{O_2}$$ $$ = 6.023 \times {10^{23}}\,\,{\text{molecules}}$$
$$\eqalign{
& 40\,\,g\,\,{\text{of}}\,\,{O_2} = \frac{{6.023 \times {{10}^{23}} \times 40}}{{32}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 7.529 \times {10^{23}}{\text{molecules}} \cr} $$
$${\text{Mass of}}\,\,6.023 \times {10^{23}}$$ $${\text{molecules}}\,\,{\text{of}}\,\,C{O_2} = 44\,g$$
$${\text{Mass of}}\,\,7.529 \times {10^{23}}$$ $${\text{molecules}}\,\,{\text{of}}\,\,C{O_2}$$ $$ = \frac{{44 \times 7.529 \times {{10}^{23}}}}{{6.023 \times {{10}^{23}}}} = 55\,g$$