Question

A solution of methanol is prepared by dissolving \(35.0 \mathrm{~mL}\) of methanol in sufficient water to give a total volume of \(115.0 \mathrm{~mL}\). What is the percent-by-volume concentration of methanol?

Short answer

The percent-by-volume concentration of methanol in the solution is approximately 30.4%

Step-by-step solution

Identify the given values

The volume of methanol (solute) is given as 35.0 mL, and the total volume of the solution is given as 115.0 mL.

Setup the formula for percent-by-volume concentration

The formula for percent-by-volume concentration of a solute is \((\frac{Volume\,of\,solute}{Total\,volume\,of\,solution}) \times 100\%\).

Substitute the values into the formula

Substitute the given values into the formula: \((\frac{35.0 \mathrm{~mL}}{115.0 \mathrm{~mL}}) \times 100\% = X\%\).

Calculate the concentration

Perform the division, multiply by 100 and round to the appropriate number of significant figures to find the percent-by-volume concentration: \(X=30.43\% \approx 30.4\%\).

Key concepts

Solution Concentration

Understanding the concentration of a solution is essential in many areas of chemistry and day-to-day applications. Solution concentration refers to the amount of a substance, known as the solute, present in a mixture. In chemistry, there are various ways to express this concentration, with percent-by-volume being a common method for liquid solutions.

Percent-by-volume concentration is calculated by taking the volume of the solute and dividing it by the total volume of the solution, then multiplying the result by 100 to convert it to a percentage. This gives us a clear picture of the proportion of solute in the mixture. For example, if a solution contains 10mL of alcohol in 100mL of water, its percent-by-volume concentration is 10%. This is a straightforward concept, yet crucial, as it helps determine the strength and dosage of the solution for various uses.

Volume of Solute

In the context of percent-by-volume concentration, the volume of solute is the amount of a dissolved substance present in a solution. It's vital to accurately measure this volume to determine the solution's concentration. Precision in measuring the volume of the solute ensures the accuracy of concentration calculations. This is especially important in sensitive experiments where the outcome may significantly depend on the solute concentration.

When preparing a solution, one might add a solute to a solvent until the desired concentration is reached, measuring in milliliters (mL) using graduated cylinders or pipettes for precision. It is fundamental to know that the solute and solvent together make up the total solution volume. For instance, if you add 35.0 mL of methanol to enough water to total 115.0 mL, you are mixing the solute with the solvent to produce the final solution.

Significant Figures

The concept of significant figures is applied in scientific measurements to indicate the precision of a number. Significant figures consist of all the digits in a number that are known with certainty plus the first uncertain digit. In chemistry, maintaining the correct number of significant figures in calculations is crucial for accuracy and reliability of results.

To determine the number of significant figures, one should start from the left with the first non-zero digit. For example, in 115.0 mL the significant figures are four, because the zeros signify that the measurement is precise to the tenth place. Following the rules of significant figures is essential when performing calculations, such as when finding the percent-by-volume concentration, to ensure that the results presented do not imply an unrealistic level of precision. Thus, when working with measurements like 35.0 mL of methanol diluted to 115.0 mL of solution, maintaining the correct number of significant figures is as important as the measurement itself.