To solve the question, we need to evaluate the assertion and reason given in the statement.
### Step 1: Understand the Assertion
The assertion states that a 1M (molar) solution and a 1m (molal) solution contain the same mass of solute.
- **Molarity (M)** is defined as the number of moles of solute per liter of solution. Therefore, a 1M solution contains 1 mole of solute in 1 liter of solution.
- **Molality (m)** is defined as the number of moles of solute per kilogram of solvent. Therefore, a 1m solution contains 1 mole of solute in 1 kilogram of solvent.
Since both solutions contain 1 mole of solute, we can calculate the mass of the solute.
### Step 2: Calculate the Mass of Solute
To find the mass of solute, we use the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
Assuming the molar mass of the solute is \( M \) grams/mole, the mass of solute in both solutions is:
- For 1M solution: \( 1 \text{ mole} \times M \text{ g/mole} = M \text{ g} \)
- For 1m solution: \( 1 \text{ mole} \times M \text{ g/mole} = M \text{ g} \)
Thus, both solutions contain the same mass of solute, confirming that the assertion is **true**.
### Step 3: Understand the Reason
The reason states that a 1M and a 1m aqueous solution are equally concentrated.
To analyze this:
- A 1M solution has 1 mole of solute in 1 liter (1000 mL) of solution.
- A 1m solution has 1 mole of solute in 1 kilogram (1000 g) of solvent. Given that the density of water is approximately 1 g/mL, 1 kg of water is equivalent to 1000 mL.
However, in the case of a 1M solution, the total volume includes both solute and solvent, which means the actual volume of the solution will be slightly more than 1000 mL due to the presence of the solute.
### Step 4: Compare Concentrations
- In the 1M solution, the concentration is based on the total volume of the solution, which is slightly more than 1000 mL.
- In the 1m solution, the concentration is based solely on the solvent, which is 1000 mL.
Since the 1M solution has a greater total volume due to the solute, the concentration of the 1M solution is actually higher than that of the 1m solution. Therefore, the reason is **false**.
### Conclusion
- **Assertion**: True (Both solutions contain the same mass of solute)
- **Reason**: False (1M and 1m solutions are not equally concentrated)
### Final Answer
Assertion is true, and reason is false.
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