A student sets up the following equation to solve a problem in solution stoichiometry:
[tex]$\left(539 . \frac{mg}{dL}\right)\left(\frac{10^{-3} g}{1 mg}\right)\left(\frac{1 dL}{10^{-1} L}\right)\left(\frac{10^{-3} L}{1 mL}\right)=\text { ? }$[/tex]
Enter the units of the student's answer.
Answer (1)
Write down all the units in the expression.
Cancel out common units in the numerator and denominator.
The remaining units are m L g .
The units of the student's answer are m L g .
Explanation
Problem Setup We are given an equation with units and asked to find the resulting units after simplification. The equation is:
Given Equation ( 539. d L m g ) ( 1 m g 1 0 − 3 g ) ( 1 0 − 1 L 1 d L ) ( 1 m L 1 0 − 3 L ) = ?
Identifying Units First, let's write down all the units in the expression: d L m g ⋅ m g g ⋅ L d L ⋅ m L L
Simplifying Units Now, we simplify the units by cancelling out common units in the numerator and denominator:
m g in the numerator and m g in the denominator cancel out.
d L in the numerator and d L in the denominator cancel out.
L in the numerator and L in the denominator cancel out.
This leaves us with m L g .
Final Units Therefore, the units of the student's answer are m L g .
Examples
In chemistry, understanding units is crucial for calculating concentrations of solutions. For instance, if you dissolve a certain amount of salt (in grams) in a specific volume of water (in milliliters), expressing the concentration in g/mL helps determine the solution's density and how it will behave in reactions. This is particularly useful in titrations, where precise concentration measurements are necessary for accurate results. Knowing the units also allows for easy conversion to other concentration units like molarity or parts per million (ppm).
