Which of the following is true

Options

A. Molarity of solution is independent of temperature
B. Molarity of solution is dependent of temperature
C. Mole fraction of solute is dependent on temperature
D. The unit of molarity is mol `dm^-3`

Answer

To determine which statements about molarity and mole fraction are true, let's analyze the provided options step by step.

### Step 1: Understand Molarity
Molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters. The formula for molarity is:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]

### Step 2: Analyze Temperature Dependence of Molarity
- The number of moles of solute does not change with temperature.
- However, the volume of the solution can change with temperature due to thermal expansion or contraction.
- Since molarity depends on the volume of the solution, it is affected by temperature.

**Conclusion**: Molarity is dependent on temperature.

### Step 3: Analyze Mole Fraction
Mole fraction is defined as the ratio of the number of moles of solute to the total number of moles of both solute and solvent:
\[ \text{Mole Fraction of Solute} = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}} \]

- The number of moles of solute is independent of temperature.
- The number of moles of solvent can also be considered independent of temperature in many cases.
- However, if the solution's temperature changes significantly, it may affect the state of the solvent (like evaporation), thus indirectly affecting the mole fraction.

**Conclusion**: Mole fraction is generally considered independent of temperature, but it can be influenced by changes in the state of the solvent.

### Step 4: Units of Molarity
The unit of molarity is expressed as moles per liter, which can also be expressed in terms of decimeters:
\[ \text{Unit of Molarity} = \text{mole per liter} = \text{mole per decimeter}^3 \]

### Final Conclusions
1. **Molarity of solution is independent of temperature** - **False**
2. **Molarity of solution is dependent on temperature** - **True**
3. **Mole fraction of solute is dependent on temperature** - **False**
4. **The unit of molarity is mole per decimeter cube** - **True**

### Correct Options
The correct statements are:
- Option 2: Molarity of solution is dependent on temperature.
- Option 4: The unit of molarity is mole per decimeter cube.