To determine the number of moles of H3PO4 in 175 mL of a 3.5 M H3PO4 solution, we need to use the relationship between the concentration, volume, and amount of a solution in moles. The concentration of a solution is defined as the number of moles of solute per liter of solution. For our solution, we know the concentration is 3.5 M H3PO4. We also know the volume is 175 mL, which is 0.175 L. Using the concentration equation:
Number of moles = Concentration x Volume
We can calculate the number of moles of H3PO4 as follows:
Number of moles of H3PO4 = (3.5 mol/L) x (0.175 L) = 0.6125 mol
Step-by-Step Working
Let’s go through the full working step-by-step:
- Write down what we know:
- Concentration of H3PO4 solution = 3.5 M
- Volume of H3PO4 solution = 175 mL = 0.175 L
- Write down the equation we need:
Number of moles = Concentration x Volume
- Plug in the known values and solve:
Number of moles of H3PO4 = (3.5 mol/L) x (0.175 L) = 0.6125 mol
Therefore, the number of moles of H3PO4 in 175 mL of a 3.5 M H3PO4 solution is 0.6125 mol.
Explanation of Calculations
Let’s go through an explanation of each step in the calculation:
- The concentration of the H3PO4 solution is given as 3.5 M. This tells us there are 3.5 moles of H3PO4 present for every 1 liter of solution.
- The volume is given as 175 mL. We need to convert this to liters to match the units of concentration. 175 mL is equal to 0.175 L.
- Using the concentration equation, we can calculate the number of moles by multiplying the concentration (3.5 mol/L) by the volume (0.175 L).
- Doing this calculation gives us:
(3.5 mol/L) x (0.175 L) = 0.6125 mol
- Therefore, there are 0.6125 moles of H3PO4 present in the 175 mL volume of 3.5 M H3PO4 solution.
The key steps are recognizing the concentration is in mol/L, converting the volume to liters, and using the concentration equation correctly to calculate the final number of moles.
Common Mistakes
Some common mistakes when calculating moles from a solution concentration and volume include:
- Forgetting to convert the volume to liters to match the units of concentration
- Using the wrong equation, such as trying to use Molarity = moles/Volume instead of the concentration equation
- Mixing up the numbers for concentration and volume in the calculation
- Calculating the molar mass instead of moles – be careful to read the question closely!
To avoid these errors, it is important to pay close attention to the units, write the values and equation down step-by-step, and double check your work. Going through the calculation methodically can help identify any mix-ups before they affect your final answer.
Practice Examples
Let’s go through some practice examples to reinforce the concepts and calculation method:
Example 1
How many moles ofNaOH are in 250 mL of a 2.5 M NaOH solution?
Solution:
- Concentration of NaOH solution = 2.5 M
- Volume of NaOH solution = 250 mL = 0.250 L
- Use equation: Number of moles = Concentration x Volume
- Number of moles of NaOH = (2.5 mol/L) x (0.250 L) = 0.625 mol
Example 2
What is the number of moles of HCl in 125 mL of a 4.0 M HCl solution?
Solution:
- Concentration of HCl solution = 4.0 M
- Volume of HCl solution = 125 mL = 0.125 L
- Use equation: Number of moles = Concentration x Volume
- Number of moles of HCl = (4.0 mol/L) x (0.125 L) = 0.5 mol
Going through examples helps reinforce the conceptual understanding and allows you to practice the calculation. Be sure to check your work and confirm the units make sense at each step.
How This Concept Is Used
Calculating the number of moles of a solute from the concentration and volume is an essential skill in chemistry. Some examples of when you would use this include:
- Preparing solutions of a desired concentration – need moles to calculate the amount of solute to add.
- Determining the stoichiometry for a reaction done in solution – moles of reactants needed based on concentration and volume.
- Calibrating instruments like spectrophotometers using standard solutions.
- Determining solubility limits and saturation conditions.
- Calculating titration volumes and analyzing titration data.
Anytime you need to know the quantity of solute present in a solution, calculating the moles from the concentration and volume will be important. Mastering this technique is essential for quantitative chemistry calculations.
Common Applications
Some of the most common applications of using solution concentration and volume to determine moles include:
- Making solutions: In the lab, you’ll frequently need to prepare solutions of a specific concentration. Using the concentration equation allows you to calculate how many moles, and thus how much solute, to weigh out.
- Titration calculations: For acid-base titrations or redox titrations, you need to know the number of moles of titrant added to reach the endpoint. This requires converting the titrant’s concentration and volume to moles.
- Solubility studies: To determine solubility limits, you may prepare saturated solutions of varying volumes. Calculating moles allows you to identify the point where no more solute dissolves.
- Spectrophotometry: Samples and standards are prepared as solutions. The concentration and volume are used to find the moles and molar absorptivity of the analyte for quantitative measurements.
- Reaction stoichiometry: For reactions done in solution, calculating the moles of reactants from concentrations and volumes added is needed to determine amounts for stoichiometric calculations.
In all these examples, the concepts remain the same. The key is recognizing when you need to convert volume to moles using the concentration, and applying the calculation correctly.
Conclusion
In summary, to find the number of moles of solute in a solution from the concentration and volume:
- Make sure volume is in liters and concentration is in mol/L
- Use the equation: Moles = Concentration x Volume
- Multiply the given concentration by the volume in liters
- Be careful with units and double check your work
- Practice examples to reinforce the concept and calculation
Being able to determine the number of moles from a solution’s concentration and volume is an essential skill in chemistry and is widely applied. Mastering the technique requires a solid understanding of units and practice calculating with different values. Pay close attention to units and setting up the calculation methodically to get the correct moles of solute.
