Certainly! Let's solve each part of the question step-by-step.
### Part (a): Calculating the volume of petrol that has the same mass as 5 cm³ of mercury
1. Determine the mass of 5 cm³ of mercury:
- Density of mercury is 13.6 g/cm³.
- Volume of mercury is 5 cm³.
- Using the formula [tex]\( \text{mass} = \text{volume} \times \text{density} \)[/tex],
[tex]\[
\text{mass}_{\text{mercury}} = 5 \, \text{cm}^3 \times 13.6 \, \text{g/cm}^3 = 68 \, \text{g}
\][/tex]
2. Find the volume of petrol that has the same mass:
- Density of petrol is 0.8 g/cm³.
- Mass of petrol is the same as the mass of mercury, which is 68 g.
- Using the formula [tex]\( \text{volume} = \frac{\text{mass}}{\text{density}} \)[/tex],
[tex]\[
\text{volume}_{\text{petrol}} = \frac{68 \, \text{g}}{0.8 \, \text{g/cm}^3} = 85 \, \text{cm}^3
\][/tex]
So, the volume of petrol that has the same mass as 5 cm³ of mercury is 85 cm³.
### Part (b): Calculating the mass of petrol that has the same volume as 41 g of mercury
1. Determine the volume of 41 g of mercury:
- Density of mercury is 13.6 g/cm³.
- Mass of mercury is 41 g.
- Using the formula [tex]\( \text{volume} = \frac{\text{mass}}{\text{density}} \)[/tex],
[tex]\[
\text{volume}_{\text{mercury}} = \frac{41 \, \text{g}}{13.6 \, \text{g/cm}^3} \approx 3.015 \, \text{cm}^3
\][/tex]
2. Find the mass of petrol that has the same volume:
- Density of petrol is 0.8 g/cm³.
- Volume of petrol is the same as the volume of mercury, which is approximately 3.015 cm³.
- Using the formula [tex]\( \text{mass} = \text{volume} \times \text{density} \)[/tex],
[tex]\[
\text{mass}_{\text{petrol}} = 3.015 \, \text{cm}^3 \times 0.8 \, \text{g/cm}^3 \approx 2.412 \, \text{g}
\][/tex]
So, the mass of petrol that has the same volume as 41 g of mercury is approximately 2.412 g.
To summarize the answers:
- The volume of petrol that has the same mass as 5 cm³ of mercury is 85 cm³.
- The mass of petrol that has the same volume as 41 g of mercury is approximately 2.412 g.
