Calculate the Concentration of a Dilute Solution

How to Calculate the Concentration of a Dilute Solution

Understanding the Basic Formula

To calculate the concentration of a diluted solution, apply the formula c_1V_1 = c_2V_2. Here c_1 and V_1 are the concentration and volume of the original solution, while c_2 and V_2 represent the concentration and volume of the diluted solution, respectively. This equation is fundamental for determining how the concentration changes as the solution’s volume is adjusted.

Materials Required

The calculation requires specific data about solution volumes and concentrations. Ensure you have measurements for the original concentration (c_1), initial volume (V_1), and the final volume of the dilute solution (V_2). Accurate data recording is crucial for precise results.

Gathering and Preparing Data

Start by making a table of the known values: original concentration, volume of the concentrated solution used, and the final desired volume after dilution. This structured approach aids in visual clarity and error minimization when substituting values into the dilution formula.

Performing the Calculation

Insert the known values into the c_1V_1 = c_2V_2 formula. Solve for c_2, the unknown concentration of the diluted solution, by rearranging the equation to c_2 = (c_1V_1)/V_2. This will provide the concentration of the solution after dilution.

Calculation Example

For instance, to dilute a 1 Molar solution to obtain 5 mL of a 0.25 Molar solution, plug in the values into the equation as follows: (1 M)(V_1) = (5 mL)(0.25 M). Solving for V_1 gives V_1 = (1.25 mL)/1 M = 1.25 mL. Thus, you would use 1.25 mL of the initial solution and add enough solvent to reach a final volume of 5 mL.

This method ensures accurate dilution calculations, essential for laboratory preparations and industrial applications where precise solute concentrations are crucial.

How to Calculate the Concentration of a Dilute Solution

Determining the concentration of a diluted solution is essential for various scientific applications. To accurately perform this calculation, you can use the formula c_1V_1 = c_2V_2, which allows you to find the concentration of a solution after its dilution.

Understanding the Dilution Formula

The dilution formula c_1V_1 = c_2V_2 links the concentration and volume of the original solution (c_1 and V_1) with the concentration and volume of the diluted solution (c_2 and V_2). To solve for the concentration of the diluted solution (c_2), rearrange the formula to:

Steps to Calculate Concentration of a Diluted Solution

Start by making a table of the known values of initial concentration (c_1), initial volume (V_1), and the volume of the dilute solution (V_2). Substitute these into the rearranged formula to obtain the concentration of your dilute solution (c_2).

Example Calculation for a Diluted Solution

For instance, to calculate the diluted concentration for a solution initially containing 0.250 mol/L sodium chloride in a volume of 100 mL that is then diluted to 1.50 L, set c_1 = 0.250 mol/L and V_1 = 0.100 L. The volume after dilution is V_2 = 1.50 L. Substitute these values in the formula to get c_2 = (0.250 mol/L * 0.100 L) / 1.50 L = 0.0167 mol/L, the concentration of the diluted solution.

This method ensures precise calculation of solution concentration post-dilution, useful in chemical, biological, and industrial applications.

Steps to Calculate Concentration of a Diluted Solution

Start by making a table of the known values of initial concentration (c_1), initial volume (V_1), and the volume of the dilute solution (V_2). Substitute these into the rearranged formula to obtain the concentration of your dilute solution (c_2).

Example Calculation for a Diluted Solution

For instance, to calculate the diluted concentration for a solution initially containing 0.250 mol/L sodium chloride in a volume of 100 mL that is then diluted to 1.50 L, set c_1 = 0.250 mol/L and V_1 = 0.100 L. The volume after dilution is V_2 = 1.50 L. Substitute these values in the formula to get c_2 = (0.250 mol/L * 0.100 L) / 1.50 L = 0.0167 mol/L, the concentration of the diluted solution.

This method ensures precise calculation of solution concentration post-dilution, useful in chemical, biological, and industrial applications.

Examples of Calculating the Concentration of a Dilute Solution

Determining the concentration of dilute solutions is essential in chemistry for achieving precise results in various experiments and reactions. Below, we explore three examples that illustrate how to calculate the concentration of a dilute solution, using commonly used formulas in solution chemistry.

Example 1: Simple Dilution

Suppose you dilute 10 mL of a 1 M NaCl solution with water to a final volume of 100 mL. The concentration of the new solution can be calculated using the formula C1 * V1 = C2 * V2, where C1 and V1 are the initial concentration and volume, and C2 and V2 are the final concentration and volume respectively. Plugging in the values, 1 M * 10 mL = C2 * 100 mL. Solving for C2, the new concentration is 0.1 M.

Example 2: Serial Dilution

In a laboratory, you might perform a serial dilution where you take 1 mL of a 0.5 M sucrose solution and add it to 9 mL of water, mixing thoroughly. Then, you take 1 mL of this mixture and add it to another 9 mL of water. Calculate the final concentration after the second dilution. Starting with the first dilution, using C1 * V1 = C2 * V2, the concentration becomes 0.05 M. Repeating the calculation for the second dilution, the sucrose concentration further drops to 0.005 M.

Example 3: Concentration from Mass and Volume

If you dissolve 58.44 g of NaCl in water to make 500 mL of solution, the concentration can be calculated by first determining the molarity. Molarity (M) is calculated as moles of solute per liter of solution. The molar mass of NaCl is 58.44 g/mol, so the moles of NaCl are 58.44 g / 58.44 g/mol = 1 mol. Since the volume of the solution is 500 mL or 0.5 L, the concentration of the NaCl solution is 1 mol / 0.5 L = 2 M.

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Calculate the Concentration of a Dilute Solution

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