A chemistry student needs 20.0 mL of tetrahydrofuran for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers that the density of tetrahydrofuran is [tex]$0.889 g^{\cdot} cm ^{-3}$[/tex]. Calculate the mass of tetrahydrofuran the student should weigh out.
Round your answer to 3 significant digits.
Answer (1)
Use the formula ma ss = d e n s i t y × v o l u m e .
Substitute the given values: d e n s i t y = 0.889 c m 3 g and v o l u m e = 20.0 m L = 20.0 c m 3 .
Calculate the mass: ma ss = 0.889 c m 3 g × 20.0 c m 3 = 17.78 g .
Round the result to 3 significant digits: 17.8 g .
Explanation
Problem Analysis We are given the volume and density of tetrahydrofuran and asked to calculate the mass. We know that density is mass per unit volume, so we can rearrange this relationship to solve for mass.
Formula The formula relating mass, density, and volume is: ma ss = d e n s i t y × v o l u m e
Substitution We are given: Density = 0.889 c m 3 g Volume = 20.0 m L Since 1 m L = 1 c m 3 , we can substitute the values directly into the formula: ma ss = 0.889 c m 3 g × 20.0 c m 3
Calculation Now, we perform the calculation: ma ss = 0.889 × 20.0 = 17.78 g
Rounding We need to round the answer to 3 significant digits. The calculated mass is 17.78 g, so rounding to 3 significant digits gives us 17.8 g.
Final Answer Therefore, the mass of tetrahydrofuran the student should weigh out is 17.8 g.
Examples
In a laboratory setting, calculating the mass of a liquid needed for an experiment based on its volume and density is a common task. For instance, if a researcher needs a specific amount of a reagent for a chemical reaction, they would use the density of the reagent to convert the required volume into mass, ensuring accurate measurements and successful experiment outcomes. This principle is also applicable in everyday scenarios, such as cooking, where recipes often provide volume measurements, but precise baking may require converting these to mass for better accuracy.
