What is the molarity of a solution if 44.0 grams of solid sodium carbonate is added to enough water to make 250.0 ml of solution? Molecular mass of Na2CO3=106 gm]
The Correct Answer and Explanation is:
To calculate the molarity of a solution, we use the formula: Molarity (M)=moles of soluteliters of solution\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}
Step 1: Calculate the moles of sodium carbonate (Na₂CO₃)
We are given:
- Mass of Na₂CO₃ = 44.0 grams
- Molar mass of Na₂CO₃ = 106 g/mol
Now calculate moles: Moles of Na₂CO₃=44.0 g106 g/mol≈0.4151 mol\text{Moles of Na₂CO₃} = \frac{44.0\ \text{g}}{106\ \text{g/mol}} \approx 0.4151\ \text{mol}
Step 2: Convert the volume of solution to liters
We are given:
- Volume = 250.0 mL
250.0 mL=0.2500 L250.0\ \text{mL} = 0.2500\ \text{L}
Step 3: Calculate the molarity
Molarity=0.4151 mol0.2500 L=1.6604 mol/L\text{Molarity} = \frac{0.4151\ \text{mol}}{0.2500\ \text{L}} = 1.6604\ \text{mol/L}
✅ Final Answer: Molarity = 1.66 M (rounded to 3 significant figures)
🔍 Explanation )
Molarity is a concentration term used in chemistry to express the amount of solute (in moles) present in one liter of solution. It is commonly denoted by M and has the units mol/L. To find molarity, we need two key pieces of information: the number of moles of solute and the volume of the solution in liters.
In this case, the solute is sodium carbonate (Na₂CO₃), a white solid salt that dissolves in water. The problem gives us the mass of sodium carbonate (44.0 grams) and the final volume of the solution (250.0 mL).
First, we use the molecular mass of sodium carbonate (106 g/mol) to convert grams to moles. This conversion is critical because molarity is based on moles, not grams. 44.0 g106 g/mol≈0.4151 mol\frac{44.0\ \text{g}}{106\ \text{g/mol}} \approx 0.4151\ \text{mol}
Next, we convert the volume of the solution from milliliters to liters by dividing by 1000. This ensures consistency with the units required for molarity. 250.0 mL=0.2500 L250.0\ \text{mL} = 0.2500\ \text{L}
Finally, we divide the moles by the volume in liters: 0.41510.2500=1.66 M\frac{0.4151}{0.2500} = 1.66\ \text{M}
This means the solution has a concentration of 1.66 moles per liter of sodium carbonate. Molarity is essential in stoichiometry, titration, and reaction calculations, as it directly relates the amount of a substance to the volume it occupies in a solution.
