Among the following, which solutions contian equal numbers of millimoles ?

Options

A. 100 mL of 0.05 M `H_(2)SO_(4)`
B. 200 mL of 0.05 M NaOH
C. 100mL of 0.010 M `Na_(2)C_(2)O_(4)`
D. 200mL of 0.025 M KOH

Answer

To determine which solutions contain equal numbers of millimoles, we will calculate the number of millimoles in each solution using the formula:

\[ \text{Millimoles} = \text{Molarity (mol/L)} \times \text{Volume (L)} \times 1000 \]

This formula allows us to convert the volume from liters to milliliters, thus calculating millimoles directly.

### Step-by-Step Solution:

1. **Calculate millimoles for H2SO4:**
- Given: Volume = 100 ml, Molarity = 0.05 M
- Convert volume to liters: \( 100 \, \text{ml} = 0.1 \, \text{L} \)
- Millimoles = \( 0.05 \, \text{mol/L} \times 0.1 \, \text{L} \times 1000 = 5 \, \text{millimoles} \)

2. **Calculate millimoles for NaOH:**
- Given: Volume = 200 ml, Molarity = 0.05 M
- Convert volume to liters: \( 200 \, \text{ml} = 0.2 \, \text{L} \)
- Millimoles = \( 0.05 \, \text{mol/L} \times 0.2 \, \text{L} \times 1000 = 10 \, \text{millimoles} \)

3. **Calculate millimoles for Na2C2O4:**
- Given: Volume = 100 ml, Molarity = 0.01 M
- Convert volume to liters: \( 100 \, \text{ml} = 0.1 \, \text{L} \)
- Millimoles = \( 0.01 \, \text{mol/L} \times 0.1 \, \text{L} \times 1000 = 1 \, \text{millimole} \)

4. **Calculate millimoles for KOH:**
- Given: Volume = 200 ml, Molarity = 0.025 M
- Convert volume to liters: \( 200 \, \text{ml} = 0.2 \, \text{L} \)
- Millimoles = \( 0.025 \, \text{mol/L} \times 0.2 \, \text{L} \times 1000 = 5 \, \text{millimoles} \)

### Summary of Results:
- H2SO4: 5 millimoles
- NaOH: 10 millimoles
- Na2C2O4: 1 millimole
- KOH: 5 millimoles

### Conclusion:
The solutions that contain equal numbers of millimoles are:
- H2SO4 (5 millimoles)
- KOH (5 millimoles)