To determine the density of the lead shots, we need to find the mass of the lead shots first and then the volume they occupy. We can use the given data to achieve this.
Given:
- Volume of the density bottle = \( 75 \, \text{cm}^3 \)
- Mass of the empty density bottle = \( 30.0 \, \text{g} \)
- Mass of the density bottle + lead shots + water = \( 156 \, \text{g} \)
- Mass of the density bottle + lead shots = \( 111 \, \text{g} \)
Let's break it down step by step:
1. **Calculate the mass of the lead shots:**
The mass of the lead shots alone can be found by subtracting the mass of the empty bottle from the mass of the bottle with the lead shots.
\[
\text{Mass of lead shots} = \text{Mass of bottle + lead shots} - \text{Mass of empty bottle}
\]
\[
= 111 \, \text{g} - 30.0 \, \text{g} = 81 \, \text{g}
\]
2. **Calculate the mass of the water:**
The mass of the water alone can be found by subtracting the mass of the bottle with the lead shots from the mass of the bottle with the lead shots and water.
\[
\text{Mass of water} = \text{Mass of bottle + lead shots + water} - \text{Mass of bottle + lead shots}
\]
\[
= 156 \, \text{g} - 111 \, \text{g} = 45 \, \text{g}
\]
3. **Calculate the volume of the water:**
Since the density of water is \( 1 \, \text{g/cm}^3 \), the volume of the water in cm\(^3\) is equal to its mass in grams.
\[
\text{Volume of water} = 45 \, \text{cm}^3
\]
4. **Calculate the volume of the lead shots:**
The volume of the lead shots can be found by subtracting the volume of the water from the total volume of the density bottle.
\[
\text{Volume of lead shots} = \text{Volume of density bottle} - \text{Volume of water}
\]
\[
= 75 \, \text{cm}^3 - 45 \, \text{cm}^3 = 30 \, \text{cm}^3
\]
5. **Calculate the density of the lead shots:**
Density is defined as mass per unit volume.
\[
\text{Density of lead shots} = \frac{\text{Mass of lead shots}}{\text{Volume of lead shots}}
\]
\[
= \frac{81 \, \text{g}}{30 \, \text{cm}^3} = 2.7 \, \text{g/cm}^3
\]
Therefore, the density of the lead shots is \( 2.7 \, \text{g/cm}^3 \).
27. In an experiment to determine the density of lead shots using a density bottle of volume 75cm3.The following data was obtained. mass of empty density bottle = 30.0g, mass of density bottle, lead shots and water =156 g, mass of density bottle + lead shots =111g. Determine the density of the lead shots.
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