A solution of metal salt was electrolysed for 15 minutes with a current of 1.5 A. The mass of the metal deposited was 0.000783 kg. Calculate the equivalent mass of the metal.

Explanation

To calculate the equivalent mass of the metal deposited during the electrolysis, we can follow these steps:

### Step 1: Convert the time from minutes to seconds
Given that the time of electrolysis is 15 minutes, we need to convert this into seconds.

\[ T = 15 \text{ minutes} \times 60 \text{ seconds/minute} = 900 \text{ seconds} \]

**Hint:** Always convert time into seconds when using formulas in electrochemistry.

### Step 2: Use the formula for the mass of the metal deposited
The mass of the metal deposited (W) can be calculated using the formula:

\[ W = Z \times I \times T \]

Where:
- \(W\) = mass of the metal deposited (in kg)
- \(Z\) = electrochemical equivalent (in kg/C)
- \(I\) = current (in A)
- \(T\) = time (in seconds)

### Step 3: Rearrange the formula to find the electrochemical equivalent (Z)
We can rearrange the formula to solve for \(Z\):

\[ Z = \frac{W}{I \times T} \]

### Step 4: Substitute the known values into the formula
Now, we can substitute the known values into the rearranged formula:

- \(W = 0.000783 \text{ kg}\)
- \(I = 1.5 \text{ A}\)
- \(T = 900 \text{ seconds}\)

\[ Z = \frac{0.000783 \text{ kg}}{1.5 \text{ A} \times 900 \text{ seconds}} \]

### Step 5: Calculate Z
Now, calculate \(Z\):

\[ Z = \frac{0.000783}{1350} \approx 5.8 \times 10^{-6} \text{ kg/C} \]

### Step 6: Relate Z to the equivalent mass (M)
The electrochemical equivalent \(Z\) can also be expressed in terms of the equivalent mass (M) and Faraday's constant (F):

\[ Z = \frac{M}{F} \]

Where \(F = 96500 \text{ C/mol}\).

### Step 7: Rearrange to find the equivalent mass (M)
Rearranging gives us:

\[ M = Z \times F \]

### Step 8: Substitute Z into the equation
Now substitute \(Z\) and \(F\) into the equation:

\[ M = (5.8 \times 10^{-6} \text{ kg/C}) \times 96500 \text{ C/mol} \]

### Step 9: Calculate M
Now calculate \(M\):

\[ M \approx 0.0559 \text{ kg/mol} = 55.9 \text{ g/mol} \]

### Final Answer
The equivalent mass of the metal is approximately **55.9 g/mol**.

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