The volume of a substance is `20"cm"^(3)` . The mass of the substance if its relative density id `2.5` will be

Options

A. `5` g
B. `50` g
C. `500` g
D. `5` kg

Explanation

To find the mass of a substance given its volume and relative density, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Volume of the substance, \( V_s = 20 \, \text{cm}^3 \)
- Relative density (RD) of the substance, \( RD = 2.5 \)

2. **Understand the Concept of Relative Density:**
- Relative density (RD) is defined as the ratio of the density of the substance (\( \rho_s \)) to the density of water (\( \rho_w \)).
- Mathematically, this can be expressed as:
\[ RD = \frac{\rho_s}{\rho_w} \]

3. **Use the Density of Water:**
- The density of water at 4°C is approximately \( 1 \, \text{g/cm}^3 \).
- Therefore, we can write:
\[ 2.5 = \frac{\rho_s}{1 \, \text{g/cm}^3} \]

4. **Calculate the Density of the Substance:**
- Rearranging the equation gives:
\[ \rho_s = 2.5 \times 1 \, \text{g/cm}^3 = 2.5 \, \text{g/cm}^3 \]

5. **Use the Density Formula:**
- The formula for density is:
\[ \rho_s = \frac{m_s}{V_s} \]
- Where \( m_s \) is the mass of the substance and \( V_s \) is the volume of the substance.

6. **Rearranging to Find Mass:**
- Rearranging the formula to find mass gives:
\[ m_s = \rho_s \times V_s \]

7. **Substituting the Values:**
- Substitute the values of density and volume:
\[ m_s = 2.5 \, \text{g/cm}^3 \times 20 \, \text{cm}^3 \]

8. **Calculating the Mass:**
- Performing the multiplication:
\[ m_s = 50 \, \text{g} \]

9. **Final Answer:**
- The mass of the substance is \( 50 \, \text{grams} \).

### Summary:
The mass of the substance is \( 50 \, \text{grams} \).

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