Calculating Original Molar Concentration Of HCl And Solution Volume
In this comprehensive guide, we will delve into the step-by-step calculation of the original molar concentration of hydrochloric acid (HCl) and the volume of the solution required for a specific preparation. This is a fundamental concept in chemistry, particularly in quantitative analysis and solution preparation. Understanding these calculations is crucial for students, researchers, and professionals in the field of chemistry.
Understanding the Problem
Before we dive into the calculations, let's first understand the problem at hand. We have a scenario where 10 ml of an HCl solution was diluted to 250 ml. Subsequently, 20.8 ml of this diluted solution was titrated with 22.8 ml of a 0.0933 mol/L NaOH solution. The objective is to determine the original molar concentration of the acid and the volume of the original HCl solution required for a specific preparation. This involves understanding the principles of dilution, titration, and stoichiometry.
Step 1: Calculate the Moles of NaOH Used in Titration
To begin, we need to calculate the number of moles of sodium hydroxide (NaOH) used in the titration. This is a crucial first step as it allows us to determine the moles of HCl that reacted with the NaOH. Molarity, a measure of concentration, is defined as the number of moles of solute per liter of solution. In this case, we know the molarity of the NaOH solution and the volume used in the titration. We can use the formula:
Moles = Molarity × Volume
Here, the molarity of the NaOH solution is given as 0.0933 mol/L, and the volume used is 22.8 ml. However, since molarity is expressed in moles per liter, we need to convert the volume from milliliters to liters. To do this, we divide the volume in milliliters by 1000:
Volume in Liters = 22.8 ml / 1000 = 0.0228 L
Now, we can calculate the moles of NaOH used:
Moles of NaOH = 0.0933 mol/L × 0.0228 L = 0.002127 moles
This calculation is fundamental as it links the known quantity of NaOH to the unknown quantity of HCl in the diluted solution. The accurate determination of moles of NaOH is paramount for the subsequent steps in the calculation.
Step 2: Determine the Moles of HCl in the Titrated Solution
The next step is to determine the number of moles of hydrochloric acid (HCl) in the 20.8 ml of the diluted solution that was titrated. This step relies on the stoichiometry of the reaction between HCl and NaOH. The reaction between HCl and NaOH is a neutralization reaction, which can be represented by the following balanced chemical equation:
HCl + NaOH → NaCl + H2O
From the balanced equation, we can see that the reaction between HCl and NaOH occurs in a 1:1 molar ratio. This means that one mole of HCl reacts with one mole of NaOH. Therefore, the number of moles of HCl in the titrated solution is equal to the number of moles of NaOH used in the titration. From the previous step, we calculated that 0.002127 moles of NaOH were used in the titration. Thus:
Moles of HCl = Moles of NaOH = 0.002127 moles
This equivalence is crucial for determining the concentration of HCl in the diluted solution. The 1:1 stoichiometry simplifies the calculation and provides a direct relationship between the reactants.
Step 3: Calculate the Molarity of HCl in the Diluted Solution
Now that we know the number of moles of HCl in the 20.8 ml of the diluted solution, we can calculate the molarity of HCl in the diluted solution. Molarity, as mentioned earlier, is defined as the number of moles of solute per liter of solution. We have the moles of HCl (0.002127 moles) and the volume of the solution (20.8 ml). Again, we need to convert the volume from milliliters to liters:
Volume in Liters = 20.8 ml / 1000 = 0.0208 L
Now, we can calculate the molarity of the diluted HCl solution using the formula:
Molarity = Moles / Volume
Molarity of Diluted HCl = 0.002127 moles / 0.0208 L = 0.1023 mol/L
This molarity represents the concentration of HCl in the diluted solution after the initial 10 ml of HCl was diluted to 250 ml. This value is an intermediate step in determining the original concentration of the HCl solution.
Step 4: Determine the Total Moles of HCl in the 250 ml Diluted Solution
To find the original concentration of the HCl solution, we need to determine the total number of moles of HCl in the 250 ml of the diluted solution. We know the molarity of the diluted solution (0.1023 mol/L) and the volume (250 ml). We convert the volume to liters:
Volume in Liters = 250 ml / 1000 = 0.250 L
Now, we can calculate the total moles of HCl in the diluted solution:
Moles = Molarity × Volume
Moles of HCl in 250 ml = 0.1023 mol/L × 0.250 L = 0.02558 moles
This value represents the total amount of HCl present in the 250 ml of the diluted solution. Since this diluted solution was made from the original 10 ml HCl solution, this number of moles is crucial for determining the original concentration.
Step 5: Calculate the Original Molar Concentration of HCl
Now we can calculate the original molar concentration of the hydrochloric acid (HCl) solution. We know that the 0.02558 moles of HCl were originally present in 10 ml of the solution. To find the molarity, we need to divide the number of moles by the volume in liters. First, we convert the volume from milliliters to liters:
Volume in Liters = 10 ml / 1000 = 0.010 L
Now, we can calculate the original molar concentration using the formula:
Molarity = Moles / Volume
Original Molarity of HCl = 0.02558 moles / 0.010 L = 2.558 mol/L
Therefore, the original molar concentration of the HCl solution was 2.558 mol/L. This is the final answer to the first part of the problem. The accurate calculation of the original molarity is essential for various applications, including solution preparation and quantitative analysis.
Step 6: Calculate the Volume of Original HCl Solution Needed for a Specific Preparation
The final step involves calculating the volume of the original HCl solution needed for a specific preparation. This requires defining the desired molarity and volume of the final solution. For the sake of demonstration, let’s assume we need to prepare 500 ml of a 0.1 mol/L HCl solution. To find the volume of the original HCl solution needed, we can use the dilution equation:
M1V1 = M2V2
Where:
- M1 is the molarity of the original solution (2.558 mol/L)
- V1 is the volume of the original solution needed (what we want to find)
- M2 is the desired molarity of the final solution (0.1 mol/L)
- V2 is the desired volume of the final solution (500 ml)
First, we need to convert the volume of the final solution from milliliters to liters:
Volume in Liters = 500 ml / 1000 = 0.5 L
Now, we can rearrange the dilution equation to solve for V1:
V1 = (M2V2) / M1
Substitute the known values:
V1 = (0.1 mol/L × 0.5 L) / 2.558 mol/L
V1 = 0.01955 L
Finally, convert the volume from liters to milliliters:
V1 = 0.01955 L × 1000 = 19.55 ml
Therefore, to prepare 500 ml of a 0.1 mol/L HCl solution, you would need 19.55 ml of the original 2.558 mol/L HCl solution. This calculation demonstrates the practical application of dilution principles in chemistry.
Conclusion
In this detailed guide, we have demonstrated the step-by-step calculations required to determine the original molar concentration of an HCl solution and the volume of that solution needed for a specific preparation. These calculations are fundamental to quantitative chemistry and are essential skills for anyone working in chemical laboratories or related fields. By understanding the principles of dilution, titration, and stoichiometry, one can accurately prepare solutions of desired concentrations, which is crucial for various scientific and industrial applications.
From calculating the moles of NaOH used in titration to applying the dilution equation, each step is critical for achieving accurate results. This guide serves as a valuable resource for students, educators, and professionals seeking a comprehensive understanding of these essential chemical calculations. Remember, precision in these calculations is paramount for the success of experiments and analyses in chemistry.
