The mass of NaNO3 (molar mass 85.00 g/mol) present in 275mL of a 0.45M solution is equal to _____g.
The correct answer and explanation is :
To find the mass of sodium nitrate (NaNO₃) in a given volume of solution, we use the formula:
[
\text{Mass (g)} = \text{Molarity (mol/L)} \times \text{Volume (L)} \times \text{Molar Mass (g/mol)}
]
Step-by-step Calculation:
- Molarity (M) = 0.45 mol/L
- Volume (V) = 275 mL = 0.275 L (since 1000 mL = 1 L)
- Molar Mass of NaNO₃ = 85.00 g/mol
Now plug into the formula:
[
\text{Mass} = 0.45 \, \text{mol/L} \times 0.275 \, \text{L} \times 85.00 \, \text{g/mol}
]
[
\text{Mass} = 10.509375 \, \text{g}
]
Rounded to three significant figures (based on the given data), the mass is:
[
\boxed{10.5 \, \text{g}}
]
Explanation (Approx. 300 Words):
In chemistry, calculating the mass of a solute (the substance dissolved in a solution) is a fundamental skill, especially in preparing or analyzing solutions. In this example, we’re working with sodium nitrate (NaNO₃), a common salt used in fertilizers and food preservation.
We’re given the molarity (concentration) of the solution as 0.45 M, which means there are 0.45 moles of NaNO₃ dissolved in every liter of solution. We’re also given the volume of the solution as 275 mL, which must be converted to liters because molarity is expressed in moles per liter. So, 275 mL is equivalent to 0.275 liters.
Next, we apply the relationship:
[
\text{moles} = \text{molarity} \times \text{volume}
]
So the moles of NaNO₃ present are:
[
0.45 \, \text{mol/L} \times 0.275 \, \text{L} = 0.12375 \, \text{mol}
]
To convert moles to grams, we multiply by the molar mass (85.00 g/mol), giving:
[
0.12375 \times 85.00 = 10.509375 \, \text{g}
]
Rounded to appropriate significant figures, the mass of NaNO₃ is 10.5 grams. This calculation is essential in laboratory settings, where accurate concentrations are required for reactions, titrations, or formulation of chemical solutions.