The resistance of two electrolytes X and Y ere found to be 45 and 100 respectively when equal volumes of both the solutions were taken in the same cell in two different experiments. If equal volumes of these solutions are mixed in the same cell, what will be the conductance of the mixture?

Explanation

To find the conductance of the mixture of two electrolytes X and Y, we can follow these steps:

### Step 1: Understand the relationship between resistance and conductance
Conductance (G) is the reciprocal of resistance (R). Therefore, we can express conductance as:
\[ G = \frac{1}{R} \]

### Step 2: Calculate the conductance of each electrolyte
Given the resistances:
- Resistance of electrolyte X, \( R_X = 45 \, \Omega \)
- Resistance of electrolyte Y, \( R_Y = 100 \, \Omega \)

We can calculate the conductance for each electrolyte:
- For electrolyte X:
\[ G_X = \frac{1}{R_X} = \frac{1}{45} \, \text{S} \]
- For electrolyte Y:
\[ G_Y = \frac{1}{R_Y} = \frac{1}{100} \, \text{S} \]

### Step 3: Find the total conductance when equal volumes are mixed
When equal volumes of both solutions are mixed, the total conductance of the mixture (G_mix) can be calculated by averaging the conductances of the two electrolytes:
\[ G_{mix} = \frac{G_X + G_Y}{2} \]

### Step 4: Substitute the values into the equation
Substituting the conductance values we found:
\[ G_{mix} = \frac{\frac{1}{45} + \frac{1}{100}}{2} \]

### Step 5: Calculate the total conductance
To add the fractions, we need a common denominator. The least common multiple of 45 and 100 is 900. Thus:
\[ \frac{1}{45} = \frac{20}{900} \]
\[ \frac{1}{100} = \frac{9}{900} \]
Now we can add these:
\[ G_{mix} = \frac{\frac{20}{900} + \frac{9}{900}}{2} = \frac{\frac{29}{900}}{2} = \frac{29}{1800} \]

### Step 6: Final calculation
Now, we can calculate the numerical value:
\[ G_{mix} \approx 0.0161 \, \text{S} \]

### Conclusion
The conductance of the mixture of the two electrolytes is approximately \( 0.0161 \, \text{S} \).