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Question: \(80{\text{ g}}\) of oxygen contains as many atoms as in A. \(80{\text{ g}}\) of hydrogen B. \(1...

80 g80{\text{ g}} of oxygen contains as many atoms as in
A. 80 g80{\text{ g}} of hydrogen
B. 1 g1{\text{ g}} of hydrogen
C. 10 g10{\text{ g}} of hydrogen
D. 5 g5{\text{ g}} of hydrogen

Explanation

Solution

We know that the amount of substance having exactly the same number of atoms as are present in 12 g12{\text{ g}} of C12{{\text{C}}^{{\text{12}}}} is known as mole. Moles is the ratio of the mass of substance in g to the molar mass of the substance in g/mol{\text{g/mol}}.

Formula Used:
Number of moles(mol) = Mass(g)Molar mass(g/mol){\text{Number of moles}}\left( {{\text{mol}}} \right){\text{ = }}\dfrac{{{\text{Mass}}\left( {\text{g}} \right)}}{{{\text{Molar mass}}\left( {{\text{g/mol}}} \right)}}

Complete step by step solution:
First we will calculate the number of moles of oxygen in 80 g80{\text{ g}} of oxygen using the formula for the number of moles.
The molar mass of oxygen is 16 g/mol16{\text{ g/mol}}. Thus,
Number of moles of oxygen = 80 g16 g/mol{\text{Number of moles of oxygen = }}\dfrac{{{\text{80 g}}}}{{{\text{16 g/mol}}}}
Number of moles of oxygen=5 mol{\text{Number of moles of oxygen}} = 5{\text{ mol}}
Thus, the number of moles of oxygen in 80 g80{\text{ g}} of oxygen is 5 mol5{\text{ mol}}.
We know that 1 mol{\text{1 mol}} of oxygen contains 6.022×10236.022 \times {10^{23}} atoms. Thus,
Number of oxygen atoms=5 mol×6.022×1023 atoms1 mol=30.11×1023 atoms{\text{Number of oxygen atoms}} = 5{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}} = 30.11 \times {10^{23}}{\text{ atoms}}
Thus, 80 g80{\text{ g}} of oxygen contains 30.11×1023 atoms30.11 \times {10^{23}}{\text{ atoms}} of oxygen.

a. Now, we have to calculate the moles of hydrogen in 80 g80{\text{ g}} of hydrogen. The molar mass of hydrogen is 1 g/mol1{\text{ g/mol}}. Thus,
Number of moles of hydrogen = 80 g1 g/mol=80 mol{\text{Number of moles of hydrogen = }}\dfrac{{{\text{80 g}}}}{{{\text{1 g/mol}}}} = 80{\text{ mol}}
Thus, the number of moles of hydrogen in 80 g80{\text{ g}} of hydrogen is 80 mol80{\text{ mol}}.
We know that 1 mol{\text{1 mol}} of hydrogen contains 6.022×10236.022 \times {10^{23}} atoms. Thus,
Number of hydrogen atoms=80 mol×6.022×1023 atoms1 mol=481.76×1023 atoms{\text{Number of hydrogen atoms}} = 80{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}} = 481.76 \times {10^{23}}{\text{ atoms}}
Thus, 80 g80{\text{ g}} of hydrogen contains 481.76×1023 atoms481.76 \times {10^{23}}{\text{ atoms}} of hydrogen.

b. Now, we have to calculate the moles of hydrogen in 1 g1{\text{ g}} of hydrogen. The molar mass of hydrogen is 1 g/mol1{\text{ g/mol}}. Thus,
Number of moles of hydrogen = 1 g1 g/mol=1 mol{\text{Number of moles of hydrogen = }}\dfrac{{1{\text{ g}}}}{{{\text{1 g/mol}}}} = 1{\text{ mol}}
Thus, the number of moles of hydrogen in 1 g1{\text{ g}} of hydrogen is 1 mol1{\text{ mol}}.
We know that 1 mol{\text{1 mol}} of hydrogen contains 6.022×10236.022 \times {10^{23}} atoms.
Thus, 1 g1{\text{ g}} of hydrogen contains 6.022×10236.022 \times {10^{23}} of hydrogen.

c. Now, we have to calculate the moles of hydrogen in 10 g10{\text{ g}} of hydrogen. The molar mass of hydrogen is 1 g/mol1{\text{ g/mol}}. Thus,
Number of moles of hydrogen = 10 g1 g/mol=10 mol{\text{Number of moles of hydrogen = }}\dfrac{{10{\text{ g}}}}{{{\text{1 g/mol}}}} = 10{\text{ mol}}
Thus, the number of moles of hydrogen in 10 g10{\text{ g}} of hydrogen is 10 mol10{\text{ mol}}.
We know that 1 mol{\text{1 mol}} of hydrogen contains 6.022×10236.022 \times {10^{23}} atoms. Thus,
Number of hydrogen atoms=10 mol×6.022×1023 atoms1 mol=60.22×1023 atoms{\text{Number of hydrogen atoms}} = 10{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}} = 60.22 \times {10^{23}}{\text{ atoms}}
Thus, 10 g10{\text{ g}} of hydrogen contains 60.22×1023 atoms60.22 \times {10^{23}}{\text{ atoms}} of hydrogen.

d. Now, we have to calculate the moles of hydrogen in 5 g5{\text{ g}} of hydrogen. The molar mass of hydrogen is 1 g/mol1{\text{ g/mol}}. Thus,
Number of moles of hydrogen = 5 g1 g/mol=5 mol{\text{Number of moles of hydrogen = }}\dfrac{{5{\text{ g}}}}{{{\text{1 g/mol}}}} = 5{\text{ mol}}
Thus, the number of moles of hydrogen in 5 g5{\text{ g}} of hydrogen is 5 mol5{\text{ mol}}.
We know that 1 mol{\text{1 mol}} of hydrogen contains 6.022×10236.022 \times {10^{23}} atoms. Thus,
Number of hydrogen atoms=5 mol×6.022×1023 atoms1 mol=30.11×1023 atoms{\text{Number of hydrogen atoms}} = 5{\text{ mol}} \times \dfrac{{6.022 \times {{10}^{23}}{\text{ atoms}}}}{{1{\text{ mol}}}} = 30.11 \times {10^{23}}{\text{ atoms}}
Thus, 5 g5{\text{ g}} of hydrogen contains 30.11×1023 atoms30.11 \times {10^{23}}{\text{ atoms}} of hydrogen.
Thus,
80 g80{\text{ g}} of oxygen contains 30.11×1023 atoms30.11 \times {10^{23}}{\text{ atoms}} of oxygen. And, 5 g5{\text{ g}} of hydrogen contains 30.11×1023 atoms30.11 \times {10^{23}}{\text{ atoms}} of hydrogen.
Thus,
80 g80{\text{ g}} of oxygen contains as many atoms as in 5 g5{\text{ g}} of hydrogen.

**Thus, the correct option is (D) 5 g5{\text{ g}} of hydrogen.

Note: **
The number of atoms of a compound is Avogadro’s number for 1 mole of compound. The number 6.022×10236.022 \times {10^{23}} is known as Avogadro’s number.