$\text{Volume of } 3 \, \text{M NaOH (formula weight 40 g mol}^{-1}\text{) which can be prepared from } 84 \, \text{g of NaOH is } \_\_\_\_\_ \times 10^{-1} \, \text{dm}^3.$
Correct Answer: 7
Approach Solution - 1
The problem requires determining the volume of 3 M NaOH solution that can be prepared from 84 g of NaOH. We begin by finding the number of moles of NaOH from the given mass:
1. Determine the number of moles using the formula:
moles of NaOH = mass of NaOH / molar mass of NaOH.
Given:
- Mass of NaOH = 84 g
- Molar mass of NaOH = 40 g/mol
Calculate the moles:
- moles = 84 g / 40 g/mol = 2.1 mol
2. To find the volume of a 3 M solution, use the formula: Molarity (M) = moles of solute / volume of solution in liters.
Solve for volume:
- Volume (V) = moles of NaOH / Molarity = 2.1 mol / 3 mol/L = 0.7 L
Convert volume from liters to dm³:
- 0.7 L = 0.7 dm³
3. The requested format is \( \_ \times 10^{-1} \, \text{dm}^3 \). Expressing 0.7 as 7 × 10-1 dm³ ensures it conforms to this format.
Finally, verify if this value meets the range 7,7. Given that 7 × 10-1 = 0.7, it fits the specified range.
The volume of 3 M NaOH solution that can be prepared is 7 × 10-1 dm³.
Approach Solution -2
The molarity formula is given by: \(M = \frac{n_{\text{NaOH}}}{V_{\text{sol}}},\)
where:
- \( M \) is the molarity (in mol/L),
- \( n_{\text{NaOH}} \) is the number of moles of NaOH,
- \( V_{\text{sol}} \) is the volume of the solution (in liters).
Given:
- \( M = 3 \, \text{M} \),
- Mass of NaOH = \( 84 \, \text{g} \),
- Molar mass of NaOH = \( 40 \, \text{g/mol} \).
Step 1: Calculate the number of moles of NaOH
\(n_{\text{NaOH}} = \frac{\text{Mass of NaOH}}{\text{Molar mass}} = \frac{84}{40} = 2.1 \, \text{moles}.\)
Step 2: Calculate the volume of the solution using the molarity formula
\(V_{\text{sol}} = \frac{n_{\text{NaOH}}}{M} = \frac{2.1}{3} = 0.7 \, \text{L}.\)
Expressing the volume in scientific notation:
\(V_{\text{sol}} = 7 \times 10^{-1} \, \text{L}.\)
Final Answer: \(V_{\text{sol}} = 0.7 \, \text{L or } 7 \times 10^{-1} \, \text{L}.\)
The Correct answer is: 7
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