Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
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.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.