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Answer :
Sure, let's solve the problem step by step to find out how many grams of chlorine are in 40.1 grams of pure calcium chloride.
1. Identify the chemical formula for Calcium chloride:
- Calcium chloride is represented by the formula [tex]\( \text{CaCl}_2 \)[/tex]. This means that each molecule of calcium chloride consists of 1 calcium (Ca) atom and 2 chlorine (Cl) atoms.
2. Determine the molar masses:
- The molar mass of calcium (Ca) is 40.1 g/mol.
- The molar mass of chlorine (Cl) is 35.5 g/mol. Since there are two chlorine atoms in calcium chloride, the total molar mass of chlorine in one formula unit of [tex]\( \text{CaCl}_2 \)[/tex] is [tex]\( 2 \times 35.5 \)[/tex] g/mol.
3. Calculate the molar mass of calcium chloride ([tex]\( \text{CaCl}_2 \)[/tex]):
- Molar mass of [tex]\( \text{CaCl}_2 = 40.1 \, \text{g/mol (Ca)} + 2 \times 35.5 \, \text{g/mol (Cl)} = 111.1 \, \text{g/mol} \)[/tex].
4. Calculate the mass percentage of chlorine in calcium chloride:
- Mass of chlorine in one mole of [tex]\( \text{CaCl}_2 = 2 \times 35.5 = 71 \, \text{g} \)[/tex].
- Mass percentage of Cl in [tex]\( \text{CaCl}_2 = \frac{71 \, \text{g}}{111.1 \, \text{g}} \times 100\% \)[/tex].
5. Determine the grams of chlorine in 40.1 grams of calcium chloride:
- Since the mass percentage of chlorine in [tex]\( \text{CaCl}_2 \)[/tex] is found by dividing the total mass of chlorine by the molar mass of [tex]\( \text{CaCl}_2 \)[/tex], this percentage multiplied by the given mass of calcium chloride will provide the mass of chlorine within that sample.
- Thus, the mass of chlorine in 40.1 grams of [tex]\( \text{CaCl}_2 \)[/tex] is: [tex]\(\frac{71}{111.1} \times 40.1 \approx 25.63 \, \text{grams}\)[/tex].
Given this calculation, the correct answer is not listed among the provided choices. However, based on the calculations, it appears there may have been a misalignment with the multiple-choice answers. The calculated mass of chlorine in 40.1 grams of [tex]\( \text{CaCl}_2 \)[/tex] is approximately 25.63 grams.
1. Identify the chemical formula for Calcium chloride:
- Calcium chloride is represented by the formula [tex]\( \text{CaCl}_2 \)[/tex]. This means that each molecule of calcium chloride consists of 1 calcium (Ca) atom and 2 chlorine (Cl) atoms.
2. Determine the molar masses:
- The molar mass of calcium (Ca) is 40.1 g/mol.
- The molar mass of chlorine (Cl) is 35.5 g/mol. Since there are two chlorine atoms in calcium chloride, the total molar mass of chlorine in one formula unit of [tex]\( \text{CaCl}_2 \)[/tex] is [tex]\( 2 \times 35.5 \)[/tex] g/mol.
3. Calculate the molar mass of calcium chloride ([tex]\( \text{CaCl}_2 \)[/tex]):
- Molar mass of [tex]\( \text{CaCl}_2 = 40.1 \, \text{g/mol (Ca)} + 2 \times 35.5 \, \text{g/mol (Cl)} = 111.1 \, \text{g/mol} \)[/tex].
4. Calculate the mass percentage of chlorine in calcium chloride:
- Mass of chlorine in one mole of [tex]\( \text{CaCl}_2 = 2 \times 35.5 = 71 \, \text{g} \)[/tex].
- Mass percentage of Cl in [tex]\( \text{CaCl}_2 = \frac{71 \, \text{g}}{111.1 \, \text{g}} \times 100\% \)[/tex].
5. Determine the grams of chlorine in 40.1 grams of calcium chloride:
- Since the mass percentage of chlorine in [tex]\( \text{CaCl}_2 \)[/tex] is found by dividing the total mass of chlorine by the molar mass of [tex]\( \text{CaCl}_2 \)[/tex], this percentage multiplied by the given mass of calcium chloride will provide the mass of chlorine within that sample.
- Thus, the mass of chlorine in 40.1 grams of [tex]\( \text{CaCl}_2 \)[/tex] is: [tex]\(\frac{71}{111.1} \times 40.1 \approx 25.63 \, \text{grams}\)[/tex].
Given this calculation, the correct answer is not listed among the provided choices. However, based on the calculations, it appears there may have been a misalignment with the multiple-choice answers. The calculated mass of chlorine in 40.1 grams of [tex]\( \text{CaCl}_2 \)[/tex] is approximately 25.63 grams.
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