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Answer :
To solve the problem of finding the mass of mercury at [tex]\( 20^{\circ} \text{C} \)[/tex] when you have the volume and density, follow these steps:
1. Identify what is given and what needs to be found:
- Density of mercury: [tex]\( 13.6 \, \text{g/cm}^3 \)[/tex]
- Volume of mercury: [tex]\( 97.8 \, \text{mL} \)[/tex]
- Mass of mercury: This is the value we need to find.
2. Understand the relationship between mass, density, and volume:
- The formula to calculate mass when given density and volume is:
[tex]\[
\text{mass} = \text{density} \times \text{volume}
\][/tex]
3. Check the units:
- The density is given in [tex]\( \text{g/cm}^3 \)[/tex], which is equivalent to [tex]\( \text{g/mL} \)[/tex] since [tex]\( 1 \, \text{cm}^3 = 1 \, \text{mL} \)[/tex].
- The volume is given in [tex]\( \text{mL} \)[/tex], so no conversion is necessary.
4. Perform the calculation:
[tex]\[
\text{mass} = 13.6 \, \text{g/cm}^3 \times 97.8 \, \text{mL}
\][/tex]
5. Calculate the exact mass:
[tex]\[
\text{mass} = 13.6 \times 97.8 = 1330.08 \, \text{g}
\][/tex]
6. Compare with the given options:
- (A) [tex]\( 1.33 \times 10^3 \, \text{g} \)[/tex]
- (B) [tex]\( 7.19 \, \text{g} \)[/tex]
- (C) [tex]\( 1.00 \, \text{g/mL} \)[/tex] (incorrect unit for mass)
- (D) [tex]\( 0.139 \, \text{g} \)[/tex]
- (E) None of these
The calculated mass [tex]\( 1330.08 \, \text{g} \)[/tex] is closest to option (A), which is approximately [tex]\( 1.33 \times 10^3 \, \text{g} \)[/tex], but it isn't an exact match.
7. Choose the correct option:
Since [tex]\( 1330.08 \, \text{g} \)[/tex] doesn't exactly match any of the given choices:
- The correct option is (E) none of these.
Thus, the mass of [tex]\( 97.8 \, \text{mL} \)[/tex] of mercury at [tex]\( 20^{\circ} \text{C} \)[/tex] does not match any of the provided options exactly, so the answer is:
[tex]\[ \text{(E) none of these} \][/tex]
1. Identify what is given and what needs to be found:
- Density of mercury: [tex]\( 13.6 \, \text{g/cm}^3 \)[/tex]
- Volume of mercury: [tex]\( 97.8 \, \text{mL} \)[/tex]
- Mass of mercury: This is the value we need to find.
2. Understand the relationship between mass, density, and volume:
- The formula to calculate mass when given density and volume is:
[tex]\[
\text{mass} = \text{density} \times \text{volume}
\][/tex]
3. Check the units:
- The density is given in [tex]\( \text{g/cm}^3 \)[/tex], which is equivalent to [tex]\( \text{g/mL} \)[/tex] since [tex]\( 1 \, \text{cm}^3 = 1 \, \text{mL} \)[/tex].
- The volume is given in [tex]\( \text{mL} \)[/tex], so no conversion is necessary.
4. Perform the calculation:
[tex]\[
\text{mass} = 13.6 \, \text{g/cm}^3 \times 97.8 \, \text{mL}
\][/tex]
5. Calculate the exact mass:
[tex]\[
\text{mass} = 13.6 \times 97.8 = 1330.08 \, \text{g}
\][/tex]
6. Compare with the given options:
- (A) [tex]\( 1.33 \times 10^3 \, \text{g} \)[/tex]
- (B) [tex]\( 7.19 \, \text{g} \)[/tex]
- (C) [tex]\( 1.00 \, \text{g/mL} \)[/tex] (incorrect unit for mass)
- (D) [tex]\( 0.139 \, \text{g} \)[/tex]
- (E) None of these
The calculated mass [tex]\( 1330.08 \, \text{g} \)[/tex] is closest to option (A), which is approximately [tex]\( 1.33 \times 10^3 \, \text{g} \)[/tex], but it isn't an exact match.
7. Choose the correct option:
Since [tex]\( 1330.08 \, \text{g} \)[/tex] doesn't exactly match any of the given choices:
- The correct option is (E) none of these.
Thus, the mass of [tex]\( 97.8 \, \text{mL} \)[/tex] of mercury at [tex]\( 20^{\circ} \text{C} \)[/tex] does not match any of the provided options exactly, so the answer is:
[tex]\[ \text{(E) none of these} \][/tex]
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