Answer
The compound is approximately 18.43% sulfur and 81.57% chlorine by mass.
Solution
To find the percent composition by mass of sulfur and chlorine in the compound, we can follow these steps:
1. **Calculate the total mass of the compound**: This is the sum of the masses of sulfur and chlorine.
2. **Calculate the percent composition**: This is done by dividing the mass of each element by the total mass of the compound and then multiplying by 100 to get a percentage.
### Step 1: Calculate the total mass of the compound
Let:
- Mass of sulfur (S) = 13.65 g
- Mass of chlorine (Cl) = 60.35 g
Total mass (M) can be calculated as:
\[
M = S + Cl
\]
### Step 2: Calculate the percent composition
The percent composition of each element can be calculated using the formulas:
\[
\text{Percent composition of S} = \left( \frac{S}{M} \right) \times 100
\]
\[
\text{Percent composition of Cl} = \left( \frac{Cl}{M} \right) \times 100
\]
Now, let's perform the calculations.
First, we will calculate the total mass \( M \). Then, we will calculate the percent compositions for sulfur and chlorine.
Let's proceed with the calculations.
1. Calculate the total mass \( M \):
\[
M = 13.65 + 60.35
\]
2. Calculate the percent compositions:
\[
\text{Percent composition of S} = \left( \frac{13.65}{M} \right) \times 100
\]
\[
\text{Percent composition of Cl} = \left( \frac{60.35}{M} \right) \times 100
\]
I'll perform these calculations now.
Calculate the value by following steps:
- step0: Calculate:
\(13.65+60.35\)
- step1: Add the numbers:
\(74\)
Calculate or simplify the expression \( (60.35 / (13.65 + 60.35)) * 100 \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(\frac{60.35}{\left(13.65+60.35\right)}\right)\times 100\)
- step1: Remove the parentheses:
\(\left(\frac{60.35}{13.65+60.35}\right)\times 100\)
- step2: Add the numbers:
\(\left(\frac{60.35}{74}\right)\times 100\)
- step3: Divide the terms:
\(\frac{1207}{1480}\times 100\)
- step4: Reduce the numbers:
\(\frac{1207}{74}\times 5\)
- step5: Multiply:
\(\frac{1207\times 5}{74}\)
- step6: Multiply:
\(\frac{6035}{74}\)
Calculate or simplify the expression \( (13.65 / (13.65 + 60.35)) * 100 \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(\frac{13.65}{\left(13.65+60.35\right)}\right)\times 100\)
- step1: Remove the parentheses:
\(\left(\frac{13.65}{13.65+60.35}\right)\times 100\)
- step2: Add the numbers:
\(\left(\frac{13.65}{74}\right)\times 100\)
- step3: Divide the terms:
\(\frac{273}{1480}\times 100\)
- step4: Reduce the numbers:
\(\frac{273}{74}\times 5\)
- step5: Multiply:
\(\frac{273\times 5}{74}\)
- step6: Multiply:
\(\frac{1365}{74}\)
### Step 1: Calculate the total mass of the compound
The total mass \( M \) is:
\[
M = 13.65 + 60.35 = 74 \text{ g}
\]
### Step 2: Calculate the percent compositions
1. **Percent composition of sulfur (S)**:
\[
\text{Percent composition of S} = \left( \frac{13.65}{74} \right) \times 100 \approx 18.43\%
\]
2. **Percent composition of chlorine (Cl)**:
\[
\text{Percent composition of Cl} = \left( \frac{60.35}{74} \right) \times 100 \approx 81.57\%
\]
### Final Results
- **Percent composition of sulfur**: \( \approx 18.43\% \)
- **Percent composition of chlorine**: \( \approx 81.57\% \)
Thus, the percent composition by mass of the compound is approximately 18.43% sulfur and 81.57% chlorine.
Reviewed and approved by the UpStudy tutoring team
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