Video Transcript
A student dissolves 25 grams of MgCl2 into water to produce a solution with a volume of 500 cubic centimeters. What is the concentration of the solution in moles per cubic decimeter? Give your answer to two decimal places.
The molar mass of magnesium is 24 grams per mole and chlorine is 35.5 grams per mole. In this question, we are being asked to determine the concentration of a solution. The solution is composed of the solute magnesium chloride dissolved into water, which is the solvent. We are also told that when we calculate the concentration of the solution, the units of our answer must be expressed as moles per cubic decimeter. Cubic units, such as cubic decimeters, are units used to measure volume.
When the concentration of a solution is calculated as the amount of moles of a solute dissolved per volume of a solution, it is called molar concentration or molarity. Molarity is typically defined as the number of moles of solute per liter of solution. However, one liter is equal to one cubic decimeter. When solving problems involving molarity, we can make use of the following equation. In this equation, 𝑐 is molarity, 𝑛 is the number of moles of the solute, and 𝑣 is the volume of the solution.
Before we can make use of this equation to calculate the concentration of the solution, we’ll need to make sure that the units of the measurements given in the problem are in moles and cubic decimeters. To begin, we’ll need to convert 25 grams of the solute MgCl2 to moles. Second, we’ll need to take the volume of the solution and convert it from cubic centimeters to cubic decimeters. Our last step will be to substitute our answers from step one and two into the molarity equation and solve for concentration.
In step one, we’ll need to make use of the following equation. In this equation, 𝑛 is the amount in moles, lowercase 𝑚 is the mass in grams, and capital 𝑀 is the molar mass in grams per mole. The molar mass of MgCl2 can be calculated by adding up the average molar masses of the atoms that make up a unit of the compound. One unit of MgCl2 contains one magnesium atom and two chlorine atoms.
Next, we’ll need to multiply the number of each type of atom by the average molar mass of the atom, which is provided in the problem. After adding together the average molar masses of all of the atoms, we get an answer of 95 grams per mole, which is the molar mass of MgCl2.
Now, we can substitute the molar mass of MgCl2 and the mass of MgCl2 given in the problem into the equation. We can write 𝑛 equals 25 grams divided by 95 grams per mole. After dividing, we get a result of 0.26316 moles of magnesium chloride. We should wait to round until the final step of our calculation.
In step two, we need to convert the volume of the solution from cubic centimeters to cubic decimeters. There are 1000 cubic centimeters in a cubic decimeter. To complete the conversion, we’ll need to take the volume of the solution given in the problem, which is 500 cubic centimeters, and multiply it by one cubic decimeter per 1000 cubic centimeters. This gives us a result of 0.5 cubic decimeters.
Now, we’re ready to take our answers from steps one and two and substitute them into the molarity equation. Let’s write 𝑐 equals 0.26316 moles divided by 0.5 cubic decimeters. After dividing, the result is 0.52632 moles per cubic decimeter. This is the concentration of the magnesium chloride solution. However, we need to round our answer to two decimal places. The concentration of the magnesium chloride solution is 0.53 moles per cubic decimeter.