A certain amount of a metal whose equivalent mass is 28 displaces 0.7 L of `H_(2)` at S.T.P. from an acid. Hence, mass of the element is:

Options

A. 1.75 g
B. 0.875 g
C. ` 0.51 g//cm^(3)`
D. 7.00 g

Answer

To find the mass of the metal that displaces 0.7 L of hydrogen gas (H₂) at standard temperature and pressure (STP), we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the number of moles of H₂ displaced:**
At STP, 1 mole of any gas occupies 22.4 L. Therefore, we can calculate the number of moles of H₂ in 0.7 L using the formula:
\[ \text{Number of moles of H₂} = \frac{\text{Volume of H₂}}{\text{Molar volume at STP}} = \frac{0.7 \, \text{L}}{22.4 \, \text{L/mol}} = 0.03125 \, \text{mol} \]

2. **Calculate the mass of H₂ displaced:**
The molar mass of H₂ is 2 g/mol. Thus, the mass of H₂ can be calculated as:
\[ \text{Mass of H₂} = \text{Number of moles} \times \text{Molar mass} = 0.03125 \, \text{mol} \times 2 \, \text{g/mol} = 0.0625 \, \text{g} \]

3. **Relate the mass of H₂ to the mass of the metal:**
According to the problem, the equivalent mass of the metal is given as 28 g. We can set up a proportion where the mass of H₂ displaced (0.0625 g) is related to the mass of the metal (X g):
\[ \frac{X}{0.0625} = \frac{28}{1} \]

4. **Solve for X (mass of the metal):**
Rearranging the equation gives us:
\[ X = 28 \times 0.0625 \]
\[ X = 1.75 \, \text{g} \]

5. **Conclusion:**
The mass of the metal that displaces 0.7 L of H₂ at STP is 1.75 g.

### Final Answer:
The mass of the element is **1.75 g**.