If 255 mL of a 2.25 M sucrose solution is diluted to 800.0 rnL, what is the molarity of the diluted solution?

검증된 단계별 안내

Identify the initial conditions: The initial volume \( V_1 \) is 255 mL and the initial molarity \( M_1 \) is 2.25 M.

Identify the final conditions: The final volume \( V_2 \) is 800.0 mL. The final molarity \( M_2 \) is what we need to find.

Use the dilution equation: \( M_1 \times V_1 = M_2 \times V_2 \).

Substitute the known values into the equation: \( 2.25 \times 255 = M_2 \times 800.0 \).

Solve for \( M_2 \) by dividing both sides of the equation by 800.0.

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주요 개념

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Molarity

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) and is crucial for understanding how much solute is present in a given volume of solution. In this problem, the initial molarity of the sucrose solution is given, which will be used to calculate the final concentration after dilution.

Dilution

Dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent. The dilution equation, M1V1 = M2V2, relates the initial and final molarities (M1 and M2) and volumes (V1 and V2) of the solution. This concept is essential for solving the problem, as it allows us to find the new molarity after the solution is diluted.

Volume Conversion

Volume conversion is the process of changing the units of volume to ensure consistency in calculations. In this question, the initial volume of the sucrose solution is given in milliliters (mL), and the final volume after dilution is also in mL. Understanding how to work with these units is important for accurately applying the dilution formula and calculating the final molarity.