Which aqueous solution is the most concentrated (has the highest molarity)?

• A. $0.40\mathrm{mol}$ of $N_{2}H4$ dissolved to make $1.0L$ of solution
• B. $0.50M$ $N_{2}H4$
• C. $1.0\mathrm{mol}$ of $N_{2}H4$ dissolved to make $5.0L$ of solution
• D. $25.0g$ of $N_{2}H4$ dissolved to make $2.0L$ of solution (molar mass $=32.0g/\mathrm{mol}$)

Answer: (B)

Verified step by step guidance

1. Identify the molarity formula: Molarity (M) is defined as the number of moles of solute divided by the volume of solution in liters, expressed as \(M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\).
2. Calculate the molarity for the first solution: Given 0.40 mol of \(N_2H_4\) dissolved in 1.0 L of solution, use the formula \(M = \frac{0.40\ \text{mol}}{1.0\ \text{L}}\) to find its molarity.
3. Calculate the molarity for the second solution: Given 1.0 mol of \(N_2H_4\) dissolved in 5.0 L of solution, use the formula \(M = \frac{1.0\ \text{mol}}{5.0\ \text{L}}\) to find its molarity.
4. Calculate the molarity for the third solution: First, convert grams to moles using the molar mass. Calculate moles as \(\text{moles} = \frac{25.0\ \text{g}}{32.0\ \text{g/mol}}\). Then, calculate molarity using \(M = \frac{\text{moles}}{2.0\ \text{L}}\).
5. Compare the three molarity values calculated in the previous steps to determine which solution has the highest molarity, and thus is the most concentrated.