To find the relative density of a substance, we need to follow a series of steps to calculate it. Let's go through the process methodically:
1. Determine the density of the substance:
- The density of an object is defined as its mass per unit volume.
- Given:
- Mass (weight) of the substance = 27 grams
- Volume of the substance = 1530 cm³
- The formula for density (ρ) is:
[tex]\[
\rho = \frac{\text{mass}}{\text{volume}}
\][/tex]
- Substituting the given values:
[tex]\[
\rho_{\text{substance}} = \frac{27 \text{ grams}}{1530 \text{ cm}^3}
\][/tex]
2. Calculate the density of the substance:
- Perform the division:
[tex]\[
\rho_{\text{substance}} = \frac{27}{1530} \text{ grams/cm}^3
\][/tex]
- Simplifying the fraction:
[tex]\[
\rho_{\text{substance}} \approx 0.01765 \text{ grams/cm}^3
\][/tex]
3. Determine the relative density:
- Relative density (also known as specific gravity) is the ratio of the density of the substance to the density of water at the same temperature.
- Given:
- Density of water at 4°C (ρ_water) = 1 gram/cm³
- The formula for relative density (RD) is:
[tex]\[
RD = \frac{\rho_{\text{substance}}}{\rho_{\text{water}}}
\][/tex]
- Substituting the values:
[tex]\[
RD = \frac{0.01765 \text{ grams/cm}^3}{1 \text{ gram/cm}^3}
\][/tex]
- Simplifying the ratio:
[tex]\[
RD \approx 0.01765
\][/tex]
In conclusion, the density of the substance is approximately [tex]\( 0.01765 \)[/tex] grams/cm³, and its relative density is also [tex]\( 0.01765 \)[/tex].
