Which of the following solutes will produce the largest total molality of solute particles upon addition to 1kg of water ?

Options

A. `1.0` mole `Co(NO_(3))_(2)`
B. `2.0` mole `KCl`
C. `3.0` mole `C_(2)H_(5)OH`
D. `3.0` mole of sugar

Answer

To solve the problem of determining which solute will produce the largest total molality of solute particles upon addition to 1 kg of water, we need to consider the dissociation of each solute into its constituent ions. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand Molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, we are adding solute to 1 kg of water.

### Step 2: Identify the Solutes
Let's assume the solutes provided in the options are:
1. Cobalt(II) nitrate (Co(NO3)2)
2. Potassium chloride (KCl)
3. Glucose (C6H12O6)
4. Urea (NH2CONH2)

### Step 3: Determine the Dissociation of Each Solute
- **Cobalt(II) nitrate (Co(NO3)2)**: This dissociates into 1 Co²⁺ ion and 2 NO3⁻ ions. Thus, it produces a total of 3 particles.

\[ \text{Co(NO}_3\text{)}_2 \rightarrow \text{Co}^{2+} + 2\text{NO}_3^{-} \quad \text{(3 particles)} \]

- **Potassium chloride (KCl)**: This dissociates into 1 K⁺ ion and 1 Cl⁻ ion. Thus, it produces a total of 2 particles.

\[ \text{KCl} \rightarrow \text{K}^{+} + \text{Cl}^{-} \quad \text{(2 particles)} \]

- **Glucose (C6H12O6)**: This is a non-electrolyte and does not dissociate in solution. Thus, it produces only 1 particle.

\[ \text{C}_6\text{H}_{12}\text{O}_6 \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 \quad \text{(1 particle)} \]

- **Urea (NH2CONH2)**: This is also a non-electrolyte and does not dissociate in solution. Thus, it produces only 1 particle.

\[ \text{NH}_2\text{CONH}_2 \rightarrow \text{NH}_2\text{CONH}_2 \quad \text{(1 particle)} \]

### Step 4: Calculate Total Molality of Solute Particles
Now, we can summarize the total number of particles produced by each solute:
- Cobalt(II) nitrate: 3 particles
- Potassium chloride: 2 particles
- Glucose: 1 particle
- Urea: 1 particle

### Step 5: Conclusion
Since cobalt(II) nitrate (Co(NO3)2) produces the largest number of particles (3), it will produce the largest total molality of solute particles upon addition to 1 kg of water.

Thus, the answer is **Cobalt(II) nitrate (Co(NO3)2)**.

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