Answer :
Sure! Let's tackle each part of the question step-by-step.
### 1. Density of Ester in the Volumetric Flask
We know:
- The volume of the flask is 250 mL.
- The weight of the ester is 100 grams.
To find the density of the ester, we use the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Substituting in the given values:
[tex]\[ \text{Density of Ester} = \frac{100 \text{ grams}}{250 \text{ mL}} = 0.4 \text{ g/mL} \][/tex]
### 2. Solving Equations with Significant Figures
a. [tex]\( 98.1 \times 0.03 \)[/tex]
- 98.1 has 3 significant figures.
- 0.03 has 1 significant figure.
When multiplying, the result should have the same number of significant figures as the measurement with the fewest significant figures, which is 1 in this case.
The calculated result is approximately [tex]\( 2.943 \)[/tex], but adjusting for significant figures, it should be rounded to [tex]\( 3 \)[/tex].
b. [tex]\( 57 \times 7.368 \)[/tex]
- 57 has 2 significant figures.
- 7.368 has 4 significant figures.
The result should have 2 significant figures, so the answer is rounded to [tex]\( 420 \)[/tex].
c. [tex]\( \frac{8.578}{4.33821} \)[/tex]
- 8.578 has 4 significant figures.
- 4.33821 has 6 significant figures.
The result should have 4 significant figures. The calculated value is approximately [tex]\( 1.977313 \)[/tex], so it should be rounded to [tex]\( 1.977 \)[/tex].
### 3. Significant Figures in Each Term
a. [tex]\( 1.40 \times 10^3 \)[/tex]
The number 1.40 has 3 significant figures.
b. 6.01
The number 6.01 has 3 significant figures.
This solution provides a clear understanding of how to handle density calculations and significant figures in mathematical operations.
### 1. Density of Ester in the Volumetric Flask
We know:
- The volume of the flask is 250 mL.
- The weight of the ester is 100 grams.
To find the density of the ester, we use the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Substituting in the given values:
[tex]\[ \text{Density of Ester} = \frac{100 \text{ grams}}{250 \text{ mL}} = 0.4 \text{ g/mL} \][/tex]
### 2. Solving Equations with Significant Figures
a. [tex]\( 98.1 \times 0.03 \)[/tex]
- 98.1 has 3 significant figures.
- 0.03 has 1 significant figure.
When multiplying, the result should have the same number of significant figures as the measurement with the fewest significant figures, which is 1 in this case.
The calculated result is approximately [tex]\( 2.943 \)[/tex], but adjusting for significant figures, it should be rounded to [tex]\( 3 \)[/tex].
b. [tex]\( 57 \times 7.368 \)[/tex]
- 57 has 2 significant figures.
- 7.368 has 4 significant figures.
The result should have 2 significant figures, so the answer is rounded to [tex]\( 420 \)[/tex].
c. [tex]\( \frac{8.578}{4.33821} \)[/tex]
- 8.578 has 4 significant figures.
- 4.33821 has 6 significant figures.
The result should have 4 significant figures. The calculated value is approximately [tex]\( 1.977313 \)[/tex], so it should be rounded to [tex]\( 1.977 \)[/tex].
### 3. Significant Figures in Each Term
a. [tex]\( 1.40 \times 10^3 \)[/tex]
The number 1.40 has 3 significant figures.
b. 6.01
The number 6.01 has 3 significant figures.
This solution provides a clear understanding of how to handle density calculations and significant figures in mathematical operations.
