Which of the following solutions is more concentrated than the others

Options

A. 5.3 gm of `Na_(2)CO_(3)` in 500 ml solution
B. 5 gm. of NaOH in 100 ml solution
C. 3.65 gm of HCl in 750 ml solution
D. 4.9 gm of `H_(2)SO_(4)` in 1000 ml solution

Explanation

To determine which of the given solutions is more concentrated, we need to calculate the molarity of each solution. Molarity (M) is defined as the number of moles of solute per liter of solution. Let's analyze each option step by step.

### Step 1: Calculate Molarity of Each Solution

#### Option 1: 5.3 grams of Na2CO3 in 500 ml solution
1. **Calculate Molar Mass of Na2CO3:**
- Sodium (Na): 23 g/mol × 2 = 46 g/mol
- Carbon (C): 12 g/mol × 1 = 12 g/mol
- Oxygen (O): 16 g/mol × 3 = 48 g/mol
- Total = 46 + 12 + 48 = 106 g/mol

2. **Calculate Moles of Na2CO3:**
- Moles = mass (g) / molar mass (g/mol) = 5.3 g / 106 g/mol = 0.05 moles

3. **Convert Volume to Liters:**
- Volume = 500 ml = 0.5 L

4. **Calculate Molarity:**
- Molarity (M) = moles / volume (L) = 0.05 moles / 0.5 L = 0.1 M

#### Option 2: 5 grams of NaOH in 100 ml solution
1. **Calculate Molar Mass of NaOH:**
- Sodium (Na): 23 g/mol
- Oxygen (O): 16 g/mol
- Hydrogen (H): 1 g/mol
- Total = 23 + 16 + 1 = 40 g/mol

2. **Calculate Moles of NaOH:**
- Moles = mass (g) / molar mass (g/mol) = 5 g / 40 g/mol = 0.125 moles

3. **Convert Volume to Liters:**
- Volume = 100 ml = 0.1 L

4. **Calculate Molarity:**
- Molarity (M) = moles / volume (L) = 0.125 moles / 0.1 L = 1.25 M

#### Option 3: 3.65 grams of HCl in 750 ml solution
1. **Calculate Molar Mass of HCl:**
- Hydrogen (H): 1 g/mol
- Chlorine (Cl): 35.5 g/mol
- Total = 1 + 35.5 = 36.5 g/mol

2. **Calculate Moles of HCl:**
- Moles = mass (g) / molar mass (g/mol) = 3.65 g / 36.5 g/mol = 0.1 moles

3. **Convert Volume to Liters:**
- Volume = 750 ml = 0.75 L

4. **Calculate Molarity:**
- Molarity (M) = moles / volume (L) = 0.1 moles / 0.75 L = 0.133 M

#### Option 4: 4.9 grams of H2SO4 in 1000 ml solution
1. **Calculate Molar Mass of H2SO4:**
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Sulfur (S): 32 g/mol
- Oxygen (O): 16 g/mol × 4 = 64 g/mol
- Total = 2 + 32 + 64 = 98 g/mol

2. **Calculate Moles of H2SO4:**
- Moles = mass (g) / molar mass (g/mol) = 4.9 g / 98 g/mol = 0.05 moles

3. **Convert Volume to Liters:**
- Volume = 1000 ml = 1 L

4. **Calculate Molarity:**
- Molarity (M) = moles / volume (L) = 0.05 moles / 1 L = 0.05 M

### Step 2: Compare Molarities
Now we have the molarity of each solution:
- Option 1: 0.1 M
- Option 2: 1.25 M
- Option 3: 0.133 M
- Option 4: 0.05 M

### Conclusion
The most concentrated solution is **Option 2: 5 grams of NaOH in 100 ml solution**, with a molarity of **1.25 M**.