A student sets up and solves the following equation to solve a problem in solution stoichiometry. Fill in the missing part of the student's equation. [tex]$\left(1.8 \frac{mol}{L}\right)(0.47 \square)\left(93.09 \frac{g}{mol}\right)=79 . g$[/tex]
Answer (2)
Analyze the units in the given equation.
Determine the missing unit by equating the units on both sides of the equation.
Solve for the missing unit, which is L (Liters).
The missing part of the equation is L , so the equation is ( 1.8 L m o l ) ( 0.47 L ) ( 93.09 m o l g ) = 79. g . The final answer is L .
Explanation
Problem Analysis We are given the equation ( 1.8 L m o l ) ( 0.47 □ ) ( 93.09 m o l g ) = 79. g and need to find the missing unit. Let's analyze the units to determine what is missing.
Setting up the Equation Let the missing unit be x . Then the equation becomes ( 1.8 L m o l ) ( 0.47 x ) ( 93.09 m o l g ) = 79. g
Analyzing the Units We want to find the unit x such that the units on the left side of the equation match the units on the right side of the equation. The units on the left side are L m o l ⋅ x ⋅ m o l g = L g ⋅ x
Determining the Missing Unit The units on the right side are g . Therefore, we need L g ⋅ x = g To make the units match, x must have units of L (Liters).
Final Answer Therefore, the missing part of the student's equation is L .
Examples
In chemistry, this type of calculation is used to determine the volume of a solution needed to obtain a specific mass of a substance. For example, if you need to obtain 79 grams of a compound with a molar mass of 93.09 g/mol from a solution with a concentration of 1.8 mol/L, you would use this equation to find the required volume. This is crucial in preparing solutions for experiments or reactions, ensuring accurate measurements and results. Understanding unit conversions and stoichiometry is essential for accurate chemical calculations.
The missing unit in the student's equation is liters (L). By analyzing the units and ensuring the left side of the equation matches the right side, we conclude that x = L . This indicates that 0.47 of the missing unit is liters in the context of the problem.
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