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Sagot :
To determine which substance contains the same number of atoms as in 12 g of carbon ([tex]$C$[/tex]), we need to follow these steps:
1. Determine the number of moles of carbon in 12 g:
The atomic mass of carbon ([tex]$C$[/tex]) is given as 12 g/mol. Therefore, the number of moles in 12 g of carbon is:
[tex]\[ \text{moles of C} = \frac{12 \text{ g}}{12 \text{ g/mol}} = 1 \text{ mole} \][/tex]
2. Find the mass of each substance that contains the same number of moles (1 mole) as the carbon atoms:
- For hydrogen ([tex]$H$[/tex]) with an atomic mass of 1 g/mol:
[tex]\[ \text{mass of H} = 1 \text{ mole} \times 1 \text{ g/mol} = 1 \text{ g} \][/tex]
- For magnesium ([tex]$Mg$[/tex]) with an atomic mass of 24 g/mol:
[tex]\[ \text{mass of Mg} = 1 \text{ mole} \times 24 \text{ g/mol} = 24 \text{ g} \][/tex]
- For carbon dioxide ([tex]$CO_2$[/tex]), we need to consider its molar mass:
[tex]\[ \text{Molar mass of CO}_2 = \text{Atomic mass of C} + 2 \times \text{Atomic mass of O} = 12 \text{ g/mol} + 2 \times 16 \text{ g/mol} = 44 \text{ g/mol} \][/tex]
Thus, the mass of 1 mole of [tex]$CO_2$[/tex]:
[tex]\[ \text{mass of } CO_2 = 1 \text{ mole} \times 44 \text{ g/mol} = 44 \text{ g} \][/tex]
- For sulfur ([tex]$S$[/tex]) with an atomic mass of 32 g/mol:
[tex]\[ \text{mass of S} = 1 \text{ mole} \times 32 \text{ g/mol} = 32 \text{ g} \][/tex]
3. Compare these masses with the given options:
- Option (a): 2 g of hydrogen
- We calculated that 1 mole of hydrogen is 1 g. Hence, 2 g of hydrogen contains 2 moles.
- Option (b): 12 g of magnesium
- We calculated that 1 mole of magnesium is 24 g. Hence, 12 g of magnesium contains [tex]\( \frac{12}{24} = 0.5 \)[/tex] moles.
- Option (c): 22 g of carbon dioxide
- We calculated that 1 mole of carbon dioxide is 44 g. Hence, 22 g of carbon dioxide contains [tex]\( \frac{22}{44} = 0.5 \)[/tex] moles.
- Option (d): 32 g of sulphur
- We calculated that 1 mole of sulfur is 32 g. Hence, 32 g of sulfur contains 1 mole, which is the same as the 1 mole of carbon in 12 g of carbon.
Conclusion: The correct answer is:
d. 32 g of sulphur
This is because 32 g of sulfur contains the same number of atoms as 12 g of carbon, which is 1 mole.
1. Determine the number of moles of carbon in 12 g:
The atomic mass of carbon ([tex]$C$[/tex]) is given as 12 g/mol. Therefore, the number of moles in 12 g of carbon is:
[tex]\[ \text{moles of C} = \frac{12 \text{ g}}{12 \text{ g/mol}} = 1 \text{ mole} \][/tex]
2. Find the mass of each substance that contains the same number of moles (1 mole) as the carbon atoms:
- For hydrogen ([tex]$H$[/tex]) with an atomic mass of 1 g/mol:
[tex]\[ \text{mass of H} = 1 \text{ mole} \times 1 \text{ g/mol} = 1 \text{ g} \][/tex]
- For magnesium ([tex]$Mg$[/tex]) with an atomic mass of 24 g/mol:
[tex]\[ \text{mass of Mg} = 1 \text{ mole} \times 24 \text{ g/mol} = 24 \text{ g} \][/tex]
- For carbon dioxide ([tex]$CO_2$[/tex]), we need to consider its molar mass:
[tex]\[ \text{Molar mass of CO}_2 = \text{Atomic mass of C} + 2 \times \text{Atomic mass of O} = 12 \text{ g/mol} + 2 \times 16 \text{ g/mol} = 44 \text{ g/mol} \][/tex]
Thus, the mass of 1 mole of [tex]$CO_2$[/tex]:
[tex]\[ \text{mass of } CO_2 = 1 \text{ mole} \times 44 \text{ g/mol} = 44 \text{ g} \][/tex]
- For sulfur ([tex]$S$[/tex]) with an atomic mass of 32 g/mol:
[tex]\[ \text{mass of S} = 1 \text{ mole} \times 32 \text{ g/mol} = 32 \text{ g} \][/tex]
3. Compare these masses with the given options:
- Option (a): 2 g of hydrogen
- We calculated that 1 mole of hydrogen is 1 g. Hence, 2 g of hydrogen contains 2 moles.
- Option (b): 12 g of magnesium
- We calculated that 1 mole of magnesium is 24 g. Hence, 12 g of magnesium contains [tex]\( \frac{12}{24} = 0.5 \)[/tex] moles.
- Option (c): 22 g of carbon dioxide
- We calculated that 1 mole of carbon dioxide is 44 g. Hence, 22 g of carbon dioxide contains [tex]\( \frac{22}{44} = 0.5 \)[/tex] moles.
- Option (d): 32 g of sulphur
- We calculated that 1 mole of sulfur is 32 g. Hence, 32 g of sulfur contains 1 mole, which is the same as the 1 mole of carbon in 12 g of carbon.
Conclusion: The correct answer is:
d. 32 g of sulphur
This is because 32 g of sulfur contains the same number of atoms as 12 g of carbon, which is 1 mole.
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