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Calculating Molarity Molarity is the ratio between the moles of dissolved solute and the volume of solution in liters. The accepted volume of the solution is 1 L, so a 1M (molar) solution would be: 1M = 1 mole of solute/1 L solution Molarity is a way of determining the concentration of a solution. For example, if I wanted to know how strong a cup of coffee was, and I knew the molar mass of coffee, by calculating the molarity of the coffee, I could determine its strength. In molarity problems, the common equation is, as brought up earlier: __M = # of moles/# Liters of solution There are three variables or unknowns in molarity problems, the molarity of substance, the number of moles in the solution, and the volume of the solution. Here is how to solve with each.
Molarity Determine the molarity of a 250 ml solution containing 16 g of sulfur. Step 1: Find the molar mass of sulfur The molar mass, the same as the atomic mass( only in grams), of sulfur is listed on the periodic table, which can be found in the Chemistry textbook, or on worksheet. When you get it, you find that it is 32 g/mol Step 2: Determine moles of solute In order to find out the number of moles of a substance, divide the mass by the molar mass. In this case, you would divide 16g, the mass of the sulfur, by 32g, the molar mass of sulfur. If you wish to review how to do this more thoroughly, Go to the Mole Conversion page 16g/32g = 0.5 moles Step 3: Convert ml to L In order to do this, you use the factor label method, if you are not comfortable with this, Review Factor Label Method in the textbook. There are 1000ml in a L, which is listed in the textbook. So, in order to convert, we divide 250 ml, the amount of solvent, by 1000 , the amount equal to the unit desired, L. 250ml/1000 = 0.25 L Step 4: Convert to 1 L In order to complete the problem, we must convert to the standard amount, one L. To do this, we divide 1000 ml, 1 L, by 250 ml, is 4. So we multiply the solvent by 4, but because we multiply the solvent by 4, in order to keep the same concentration and molarity, we have to multiply the amount of solute by 4. So we multiply 0.5 moles, the amount of solute, by 4. 4 x 0.5 moles/0.25L = 2 moles/liter Step 5: Determine the molarity The molarity of a substance is equal to the amount of moles of solute per liter of solution.We now know both the amount of moles, 2, and have 1 L of solution, so all we have to do now is solve the problem. If 1M = 1 mol/IL, then 2 mol/1L would equal 2M, which is the answer. Answer = 2M note: Since this is solving equation with two constants, it is possible to reverse the order of operations, thus in this example, one can determine the L of solution first, then multiply the grams of solute, then determine the number of moles.
# of Moles In a 4M solution of Cu, there are 2 L of solution, find the number of grams of Cu.
Step 1: Convert to 2 L and find number of moles: In order to convert to 2 L, we must multiply the 1 L solution by two. Remember, 4M refers to 4 moles per L. So, if we multply the volume of the solution by two, we must do the same to the number of moles. 4 moles/L x 2 = 8 moles/2L Step 2: Find molar mass of Cu We look up the molar mass of Cu on the periodic table in the textbook and we find it to be 63.5g/mole. Step 3: Find number of grams of Cu To do this, we multiply the number of moles by the molar mass. We figured out both in the previous two steps, so all we need to do now is multiply. 8 moles x 63.5g/mol = 508 g
# of Liters of Solution
What is the volume of a 5M solution of carbon with 360 g of solute ? Step 1 : Find molar mass of carbon We look up the molar mass of carbon on the periodic table in the textbook, and we find it to be 12g. Step 2 : Determine number of moles In order to find the number of moles, we divide the mass of the carbon by the molar mass. So, 360g/12g/mole = 30 moles Step 3: Determine number of L of solution To find the number of liters of solution, we must find out in what volume solution would a 5M solution have 30 moles of solute. In a 1 L 5M solution, there would be 5 moles of solute, in a 2L 5M solution, there would be 10 moles, etc. So we can cross multiply. 5M = 5 moles/1L = 30 moles/_L. We divide 30 moles by 5 moles, and we find the answer to be 30 moles/5 moles = 6. So we have our answer, 6 L |