# Chemistry problem with molarity and ions

• ahhppull
In summary, to precipitate both metals from hard water using a detergent mixture designed for hard water with a Molarity of 40.08g of MM Ca and 24.31g of MM Mg, the detergent should require .63kg of sodium carbonate per load of laundry.
ahhppull

## Homework Statement

Sodium carbonate is often added to laundry detergents to soften hard water and make the detergent more effective. Suppose that a particular detergent mixture is designed to soften hard water that is 3.8×10^−3 M in Ca2+ and 1.1×10^−3 M in Mg2+ and that the average capacity of a washing machine is 19.0 gallons of water.

If the detergent requires using 0.63 kg detergent per load of laundry, determine what percentage (by mass) of the detergent should be sodium carbonate in order to completely precipitate all of the calcium and magnesium ions in an average load of laundry water.

## Homework Equations

Molarity = moles/L
MM Ca = 40.08g
MM Mg = 24.31g
1 kg = .001 g
1 gal = 3.785L

## The Attempt at a Solution

I was confused about this problem, but I used 2 of my tries and have 1 try left over. My first answer was 46& and my second answer was 98% (both of these are wrong)

My method's probably wrong, but here's what I did. I started by multiplying 19 gallons by 3.785 to get 71.915 liters. Then I multiplied the molarity of Ca and Mg each by 71.915 liters to get the grams of each. Then I multiplied the moles by the MM of each of the element. Then I added these two up and added it to .63Kkg (630g) and dived 630g by the total mass.

ahhppull said:
My method's probably wrong, but here's what I did. I started by multiplying 19 gallons by 3.785 to get 71.915 liters.

No idea if conversion factor is correct, but the idea is OK.

Then I multiplied the molarity of Ca and Mg each by 71.915 liters to get the grams of each.

I guess you mean moles, not grams.

Then I multiplied the moles by the MM of each of the element. Then I added these two up and added it to .63Kkg (630g) and dived 630g by the total mass.

You calculated total mass of calcium and magnesium dissolved. That's not what you are looking for - you need to add enough sodium carbonate to precipitate both metals.

I guess you are to ignore solubility product and assume reaction goes simply to completion. What reaction? That's what you need to solve the question.

--

## 1. What is molarity and how is it calculated?

Molarity is a unit of concentration that measures the number of moles of solute per liter of solution. It is calculated by dividing the moles of solute by the volume of the solution in liters.

## 2. How do I convert between grams and moles?

To convert from grams to moles, divide the mass of the substance in grams by its molar mass. To convert from moles to grams, multiply the number of moles by the molar mass.

## 3. How do I determine the number of ions in a compound?

The number of ions in a compound can be determined by looking at its chemical formula. The subscript number next to each element represents the number of atoms present, and the charge of the ion is determined by the element's position on the periodic table.

## 4. What is the relationship between molarity and dilution?

Dilution is the process of reducing the concentration of a solute in a solution. The relationship between molarity and dilution is inversely proportional, meaning that as the volume of the solution increases, the molarity decreases.

## 5. How do I balance a chemical equation?

To balance a chemical equation, the number of atoms of each element on the reactant side must be equal to the number of atoms on the product side. This can be achieved by adjusting the coefficients in front of each molecule.

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