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To determine the number of formula units in 24.2 grams of calcium chloride (CaCl₂), we'll follow a step-by-step approach:
### Step 1: Determine the molar mass of calcium chloride
Calcium chloride (CaCl₂) consists of one calcium atom (Ca) and two chlorine atoms (Cl).
- The atomic mass of calcium (Ca) is approximately 40.08 g/mol.
- The atomic mass of chlorine (Cl) is approximately 35.45 g/mol.
So, the molar mass of calcium chloride (CaCl₂) can be calculated as:
[tex]\[ \text{Molar mass of CaCl}_2 = \text{Atomic mass of Ca} + 2 \times \text{Atomic mass of Cl} \][/tex]
[tex]\[ \text{Molar mass of CaCl}_2 = 40.08 \, \text{g/mol} + 2 \times 35.45 \, \text{g/mol} \][/tex]
[tex]\[ \text{Molar mass of CaCl}_2 = 40.08 \, \text{g/mol} + 70.90 \, \text{g/mol} \][/tex]
[tex]\[ \text{Molar mass of CaCl}_2 = 110.98 \, \text{g/mol} \][/tex]
### Step 2: Calculate the number of moles of calcium chloride in 24.2 grams
The number of moles [tex]\( n \)[/tex] can be calculated using the formula:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} \][/tex]
Given:
- Mass of calcium chloride [tex]\( = 24.2 \, \text{g} \)[/tex]
- Molar mass of calcium chloride [tex]\( = 110.98 \, \text{g/mol} \)[/tex]
So:
[tex]\[ n = \frac{24.2 \, \text{g}}{110.98 \, \text{g/mol}} \][/tex]
[tex]\[ n \approx 0.218 \, \text{moles of CaCl}_2 \][/tex]
### Step 3: Calculate the number of formula units of calcium chloride
One mole of any substance contains Avogadro's number of entities (atoms, molecules, formula units, etc.). Avogadro's number is approximately [tex]\( 6.022 \times 10^{23} \)[/tex].
Thus, the number of formula units [tex]\( N \)[/tex] can be calculated as:
[tex]\[ N = n \times \text{Avogadro's number} \][/tex]
Given the number of moles we calculated:
[tex]\[ N = 0.218 \, \text{moles} \times 6.022 \times 10^{23} \, \text{formula units/mole} \][/tex]
[tex]\[ N \approx 1.31 \times 10^{23} \, \text{formula units} \][/tex]
### Conclusion
Therefore, the number of formula units in 24.2 grams of calcium chloride is approximately [tex]\( 1.31 \times 10^{23} \)[/tex].
Given the answer choices:
- No correct answer
- [tex]\( 1.52 \times 10^{23} \)[/tex]
- [tex]\( 7.16 \times 10^{23} \)[/tex]
- [tex]\( 1.31 \times 10^{23} \)[/tex]
- [tex]\( 8.14 \times 10^{22} \)[/tex]
The correct answer is [tex]\( 1.31 \times 10^{23} \)[/tex] formula units in 24.2 grams of calcium chloride.
### Step 1: Determine the molar mass of calcium chloride
Calcium chloride (CaCl₂) consists of one calcium atom (Ca) and two chlorine atoms (Cl).
- The atomic mass of calcium (Ca) is approximately 40.08 g/mol.
- The atomic mass of chlorine (Cl) is approximately 35.45 g/mol.
So, the molar mass of calcium chloride (CaCl₂) can be calculated as:
[tex]\[ \text{Molar mass of CaCl}_2 = \text{Atomic mass of Ca} + 2 \times \text{Atomic mass of Cl} \][/tex]
[tex]\[ \text{Molar mass of CaCl}_2 = 40.08 \, \text{g/mol} + 2 \times 35.45 \, \text{g/mol} \][/tex]
[tex]\[ \text{Molar mass of CaCl}_2 = 40.08 \, \text{g/mol} + 70.90 \, \text{g/mol} \][/tex]
[tex]\[ \text{Molar mass of CaCl}_2 = 110.98 \, \text{g/mol} \][/tex]
### Step 2: Calculate the number of moles of calcium chloride in 24.2 grams
The number of moles [tex]\( n \)[/tex] can be calculated using the formula:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} \][/tex]
Given:
- Mass of calcium chloride [tex]\( = 24.2 \, \text{g} \)[/tex]
- Molar mass of calcium chloride [tex]\( = 110.98 \, \text{g/mol} \)[/tex]
So:
[tex]\[ n = \frac{24.2 \, \text{g}}{110.98 \, \text{g/mol}} \][/tex]
[tex]\[ n \approx 0.218 \, \text{moles of CaCl}_2 \][/tex]
### Step 3: Calculate the number of formula units of calcium chloride
One mole of any substance contains Avogadro's number of entities (atoms, molecules, formula units, etc.). Avogadro's number is approximately [tex]\( 6.022 \times 10^{23} \)[/tex].
Thus, the number of formula units [tex]\( N \)[/tex] can be calculated as:
[tex]\[ N = n \times \text{Avogadro's number} \][/tex]
Given the number of moles we calculated:
[tex]\[ N = 0.218 \, \text{moles} \times 6.022 \times 10^{23} \, \text{formula units/mole} \][/tex]
[tex]\[ N \approx 1.31 \times 10^{23} \, \text{formula units} \][/tex]
### Conclusion
Therefore, the number of formula units in 24.2 grams of calcium chloride is approximately [tex]\( 1.31 \times 10^{23} \)[/tex].
Given the answer choices:
- No correct answer
- [tex]\( 1.52 \times 10^{23} \)[/tex]
- [tex]\( 7.16 \times 10^{23} \)[/tex]
- [tex]\( 1.31 \times 10^{23} \)[/tex]
- [tex]\( 8.14 \times 10^{22} \)[/tex]
The correct answer is [tex]\( 1.31 \times 10^{23} \)[/tex] formula units in 24.2 grams of calcium chloride.
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