If 1 g of substance of relative density 2 and 4 g of another substance of relative density 3 are mixed together then the relative density of the mixture is

Options

A. 2.4
B. 2.5
C. 2.7
D. 2.8

Answer

To find the relative density of the mixture of two substances, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of substance 1 (m1) = 1 g
- Relative density of substance 1 (RD1) = 2
- Mass of substance 2 (m2) = 4 g
- Relative density of substance 2 (RD2) = 3

2. **Calculate the Densities of Each Substance:**
- The density of a substance can be calculated using the formula:
\[ \text{Density} = \text{Relative Density} \times \text{Density of Water} \]
- For substance 1:
\[ \rho_1 = RD1 \times \rho_w = 2 \times \rho_w \]
- For substance 2:
\[ \rho_2 = RD2 \times \rho_w = 3 \times \rho_w \]

3. **Calculate the Volume of Each Substance:**
- Volume can be calculated using the formula:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
- For substance 1:
\[ V_1 = \frac{m1}{\rho_1} = \frac{1}{2 \rho_w} \]
- For substance 2:
\[ V_2 = \frac{m2}{\rho_2} = \frac{4}{3 \rho_w} \]

4. **Calculate the Total Volume of the Mixture:**
- The total volume (V_total) of the mixture is the sum of the volumes of the two substances:
\[ V_{\text{total}} = V_1 + V_2 = \frac{1}{2 \rho_w} + \frac{4}{3 \rho_w} \]
- To add these fractions, find a common denominator (which is \(6 \rho_w\)):
\[ V_{\text{total}} = \frac{3}{6 \rho_w} + \frac{8}{6 \rho_w} = \frac{11}{6 \rho_w} \]

5. **Calculate the Total Mass of the Mixture:**
- The total mass (m_total) is the sum of the masses of the two substances:
\[ m_{\text{total}} = m1 + m2 = 1 + 4 = 5 \text{ g} \]

6. **Calculate the Density of the Mixture:**
- The density of the mixture (\(\rho_m\)) can be calculated using the formula:
\[ \rho_m = \frac{m_{\text{total}}}{V_{\text{total}}} \]
- Substituting the values:
\[ \rho_m = \frac{5}{\frac{11}{6 \rho_w}} = 5 \times \frac{6 \rho_w}{11} = \frac{30 \rho_w}{11} \]

7. **Calculate the Relative Density of the Mixture:**
- The relative density of the mixture (RD_m) is given by:
\[ RD_m = \frac{\rho_m}{\rho_w} = \frac{\frac{30 \rho_w}{11}}{\rho_w} = \frac{30}{11} \approx 2.727 \]

### Final Answer:
The relative density of the mixture is approximately **2.727**.

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