0.05 g of magnesium when treated with dilute HCI gave 51 mL of hydrogen at 27°C and 780 mm pressure. Calculate the equivalent mass of magnesium.

Answer

To calculate the equivalent mass of magnesium from the given data, we will follow these steps:

### Step 1: Write the reaction
The reaction between magnesium (Mg) and dilute hydrochloric acid (HCl) can be written as:
\[ \text{Mg} + 2 \text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2 \]

### Step 2: Convert the volume of hydrogen gas to liters
The volume of hydrogen gas produced is given as 51 mL. We convert this to liters:
\[ V = 51 \, \text{mL} = 0.051 \, \text{L} \]

### Step 3: Convert the temperature to Kelvin
The temperature is given as 27°C. We convert this to Kelvin:
\[ T = 27 + 273 = 300 \, \text{K} \]

### Step 4: Use the ideal gas law to find the number of moles of hydrogen gas
We use the ideal gas equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure in mmHg = 780 mmHg
- \( V \) = volume in liters = 0.051 L
- \( R \) = ideal gas constant = 62.363 mmHg L/(mol K)
- \( T \) = temperature in Kelvin = 300 K

Rearranging the equation to solve for \( n \) (number of moles):
\[ n = \frac{PV}{RT} \]

Substituting the values:
\[ n = \frac{(780 \, \text{mmHg}) \times (0.051 \, \text{L})}{(62.363 \, \text{mmHg L/(mol K)}) \times (300 \, \text{K})} \]

Calculating \( n \):
\[ n \approx 0.002126 \, \text{moles} \]

### Step 5: Relate moles of hydrogen to grams of magnesium
From the balanced equation, 1 mole of Mg produces 1 mole of H2. Therefore, the moles of magnesium that reacted to produce 0.002126 moles of H2 is also 0.002126 moles.

### Step 6: Calculate the mass of magnesium that produces 1 mole of hydrogen
Given that 0.05 grams of magnesium produces 0.002126 moles of hydrogen, we can find the mass of magnesium required to produce 1 mole of hydrogen:
\[ \text{Mass of Mg for 1 mole H2} = \frac{0.05 \, \text{g}}{0.002126 \, \text{moles}} \approx 23.518 \, \text{g} \]

### Step 7: Calculate the equivalent mass of magnesium
Since magnesium displaces 2 moles of H+ ions, the equivalent mass is calculated as:
\[ \text{Equivalent mass} = \frac{\text{Atomic mass}}{n} = \frac{23.518 \, \text{g}}{2} \approx 11.759 \, \text{g} \]

### Final Answer
The equivalent mass of magnesium is approximately **11.759 grams**.

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