16.55g of lead (ll) trioxonitrate (V) was dissolved in 100g of distilled water at 20oC, calculate the…

To solve this problem, we need to determine the concentration of the solution in moles per cubic decimeter ($mol/dm^3$).

1. Analyze the Question

• Mass of solute ($m$): 16.55 g
• Mass of solvent (water): 100 g
• Molar Mass of $Pb(NO_3)_2$: We need to calculate this using the given atomic masses ($Pb=207, N=14, O=16$).
• Goal: Calculate solubility in $mol/dm^3$.

2. Explain the Concept

Solubility in $mol/dm^3$ is calculated using the formula:

Since the mass of the solute is small compared to the water, we assume the volume of the solution is approximately equal to the volume of the water. Given that the density of water is $1 g/cm^3$, $100 g$ of water is equal to $100 cm^3$ (or $0.1 dm^3$).

3. Show the Solution

Step 1: Calculate the Molar Mass of $Pb(NO_3)_2$

• $Pb = 207$
• $N = 14 \times 2 = 28$
• $O = 16 \times 6 = 96$
• Total Molar Mass = $207 + 28 + 96 = 331 g/mol$

Step 2: Calculate the number of moles ($n$)

Step 3: Convert volume to $dm^3$ Volume = $100 cm^3 = \frac{100}{1000} dm^3 = 0.1 dm^3$

Step 4: Calculate the concentration

4. Identify the Answer

Comparing our result ($0.5$) to the options provided, the correct value is $0.50$. Note that while the unit in the question asks for $mol/dm^3$, the options are labeled with 'g'. Based on the calculation, the numerical value is 0.50.

5. Exam Tip

When dealing with solubility questions in JAMB, always remember the conversion factor: $1000 cm^3 = 1 dm^3$. If you are given the mass of water in grams, it is almost always safe to treat it as the volume in $cm^3$ for these calculations unless the density of the solution is provided.