How many grams of potassium carbonate are needed to make 400.0 mL of 2.5 M solution?
$K_2 CO_3: 138.21 g / mol$
A. $140,000 g K _{-} CO _3$
B. $86 g K _2 CO _3$
C. $140 g K = CO _3$
D. $21 g K _2 CO _3$
Answer (2)
To make 400.0 mL of a 2.5 M solution of potassium carbonate, you need 138.21 grams of K 2 C O 3 . This is determined by converting the volume to liters, calculating the moles needed, and then using the molar mass to find the mass. The correct answer is approximately 138 g, so the closest multiple-choice answer is option C, 140 g K 2 C O 3 .
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Convert the volume from mL to L: V = 400.0 ÷ 1000 = 0.4 L .
Calculate the number of moles of K 2 C O 3 : m o l es = 2.5 × 0.4 = 1.0 m o l .
Calculate the mass of K 2 C O 3 : ma ss = 1.0 × 138.21 = 138.21 g .
Therefore, the mass of potassium carbonate needed is 138.21 g .
Explanation
Problem Analysis We are asked to find the mass of potassium carbonate ( K 2 C O 3 ) needed to make 400.0 mL of a 2.5 M solution. We are given the molar mass of K 2 C O 3 as 138.21 g/mol.
Convert Volume to Liters First, we need to convert the volume from milliliters (mL) to liters (L) since molarity is defined as moles per liter. To convert mL to L, we divide by 1000: V ( L ) = 1000 V ( m L ) = 1000 400.0 = 0.4 L
Calculate Moles of Solute Next, we calculate the number of moles of K 2 C O 3 needed. Molarity (M) is defined as moles of solute per liter of solution: M = V o l u m e ( L ) m o l es We can rearrange this formula to solve for moles: m o l es = M o l a r i t y × V o l u m e ( L ) Substituting the given values: m o l es = 2.5 L m o l × 0.4 L = 1.0 m o l
Calculate Mass of Solute Now that we know the number of moles of K 2 C O 3 needed, we can calculate the mass using the molar mass: ma ss = m o l es × M o l a r ma ss Substituting the values: ma ss = 1.0 m o l × 138.21 m o l g = 138.21 g
Final Answer Therefore, 138.21 grams of potassium carbonate are needed to make 400.0 mL of a 2.5 M solution.
Examples
Potassium carbonate is often used in the production of soap and glass. If a manufacturer needs to produce a specific volume of a cleaning solution with a certain concentration of potassium carbonate, they would need to calculate the exact mass of potassium carbonate to dissolve in the solution. This ensures the final product has the desired properties and effectiveness. For example, if a soap factory wants to create 400 mL of a 2.5 M potassium carbonate solution for a new soap formula, they would need to weigh out 138.21 grams of potassium carbonate.
