How many grams of solute are dissolved in 125.0 ml of 5.00 M NaCl (MM=58.45)?
The Correct Answer and Explanation is :
To calculate the mass of solute (NaCl) dissolved in a given volume of solution, we can use the relationship between molarity, volume, and moles of solute: Molarity(M)=moles of solutevolume of solution in liters\text{Molarity} (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
We are given:
- Molarity of NaCl (M) = 5.00 M
- Volume of solution = 125.0 mL = 0.1250 L (converted from milliliters to liters)
- Molar mass (MM) of NaCl = 58.45 g/mol
Step 1: Calculate the moles of NaCl
First, rearrange the molarity equation to solve for the moles of solute: moles of NaCl=Molarity×Volume (in liters)\text{moles of NaCl} = \text{Molarity} \times \text{Volume (in liters)}
Substitute the given values: moles of NaCl=5.00 M×0.1250 L=0.625 moles\text{moles of NaCl} = 5.00 \, \text{M} \times 0.1250 \, \text{L} = 0.625 \, \text{moles}
Step 2: Convert moles to grams
Next, use the molar mass of NaCl to convert moles of NaCl to grams. The molar mass of NaCl is 58.45 g/mol, so: grams of NaCl=moles of NaCl×molar mass of NaCl\text{grams of NaCl} = \text{moles of NaCl} \times \text{molar mass of NaCl}
Substitute the values: grams of NaCl=0.625 moles×58.45 g/mol=36.56 grams\text{grams of NaCl} = 0.625 \, \text{moles} \times 58.45 \, \text{g/mol} = 36.56 \, \text{grams}
Final Answer:
The mass of NaCl dissolved in 125.0 mL of 5.00 M NaCl solution is 36.56 grams.
Explanation:
The key to solving this problem is understanding the relationship between molarity (M), moles of solute, and volume of solution. Molarity is a measure of concentration and tells us how many moles of solute are in one liter of solution. By multiplying the molarity by the volume of solution (in liters), we obtain the total number of moles of solute present. Finally, to find the mass of solute, we multiply the number of moles by the molar mass of NaCl, which tells us how many grams are in one mole of NaCl.