Fill in the missing part of the student's equation:
$\frac{(1.69 \square)(\frac{1 mL}{10^{-3} L})}{(81.19 \frac{g}{mol})}=20.8 \frac{mol}{L}$
Answer (2)
The problem requires finding the missing unit in a stoichiometry equation.
Analyze the units in the given equation to determine the missing unit.
Perform algebraic manipulations to isolate the missing unit and determine its value.
The missing unit is m L g .
Explanation
Problem Setup We are given the equation ( 81.19 m o l g ) ( 1.69 □ ) ( 1 0 − 3 L 1 m L ) = 20.8 L m o l and we need to find the missing unit.
Isolating the Unknown Let's denote the missing unit by x . Then the equation becomes ( 81.19 m o l g ) ( 1.69 x ) ( 1 0 − 3 L 1 m L ) = 20.8 L m o l We want to isolate x to determine its value and units.
Calculations and Simplification First, we multiply both sides by 81.19 m o l g :
( 1.69 x ) ( 1 0 − 3 L 1 m L ) = 20.8 L m o l × 81.19 m o l g ( 1.69 x ) ( 1 0 − 3 L 1 m L ) = 1688.752 L g Next, we divide both sides by 1.69 and 1 0 − 3 L 1 m L :
x = 1.69 × 1 0 − 3 L 1 m L 1688.752 L g = 1.69 × 1000 L m L 1688.752 L g = 1690 1688.752 m L g x ≈ 0.999 m L g However, we need to find the missing unit such that the equation holds true.
Unit Analysis Let's analyze the units in the original equation. We have: ( 81.19 m o l g ) ( 1.69 □ ) ( 1 0 − 3 L 1 m L ) = 20.8 L m o l We can rewrite 1 0 − 3 L 1 m L as 0.001 L 1 m L = 1000 L m L . So the equation becomes: ( 81.19 m o l g ) ( 1.69 □ ) ( 1000 L m L ) = 20.8 L m o l Let the missing unit be x . Then: ( 81.19 m o l g ) ( 1.69 x ) ( 1000 L m L ) = 20.8 L m o l We want to find the unit of x such that the left side has units of L m o l .
Finding the Missing Unit Let's rearrange the equation to solve for x :
1.69 x × 1000 L m L = 20.8 L m o l × 81.19 m o l g 1.69 x × 1000 L m L = 1688.752 L g x = 1.69 × 1000 L m L 1688.752 L g = 1690 1688.752 m L g = 0.999 m L g Since the result is approximately 1 m L g , let's assume the missing part is m L g . Then the equation is: ( 81.19 m o l g ) ( 1.69 m L g ) ( 1 0 − 3 L 1 m L ) = 20.8 L m o l ( 81.19 m o l g ) ( 1.69 m L g ) ( 1000 L m L ) = 20.8 L m o l 81.19 m o l g 1690 L g = 20.8 L m o l 20.815 L m o l ≈ 20.8 L m o l So the missing unit is indeed m L g .
Final Answer The missing part of the student's equation is m L g .
Examples
In chemistry, solution stoichiometry is used to calculate the amounts of reactants and products in chemical reactions involving solutions. For example, if you are titrating an acid with a base, you need to know the concentration of the base solution to determine the amount of acid in the unknown solution. The equation provided in the problem is a typical setup for such calculations, where the missing unit helps to ensure that the units on both sides of the equation are consistent, leading to a correct result. This is crucial in fields like pharmaceutical research, environmental monitoring, and chemical manufacturing, where precise measurements are essential for safety and efficiency.
The missing part of the student's equation is m L g . This conclusion was determined by isolating the unknown in the equation and performing unit analysis to ensure dimensional consistency. The final equation confirms that the units match correctly.
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