How to Calculate the Concentration of a Solution

In Chemistry, a solution is a homogeneous mixture of two things - a solute and the solvent that it's dissolved in. Concentration is a measure of how much solute is dissolved within the solvent. There are many reasons for calculating the concentration of a solution, but the chemistry involved is similar whether you're testing the chlorine level in a hot tub or performing life-saving analysis on a blood sample. This guide will teach a few of the basic fundamentals of solution chemistry, then walk you through the process of one of its common practical applications - aquarium maintenance.

EditSteps

EditLearning Concentration Basics

1. Learn the vocabulary. Concentration is a ratio comparing the amount of one substance to the amount of the entire mixture. For instance, if you plan to mix sugar and vinegar together for an experiment, you'll need to calculate the concentration of sugar in the mixture. Here's how each ingredient would be described in the chemistry report:
   
   • The sugar is the solute, which is the substance being dissolved. You are measuring the concentration of the solute.
   • The vinegar is the solvent, which is the substance you are dissolving something in.
   • After you mix them together, you end up with a solution. To calculate the concentration, you'll need to the total amount of the solution, which you can get by adding the solute and solvent quantities together.
   • If you forget which is the solute and which the solvent, remember this example. Sugar and solute both contain the letter U, while vinegar and solvent both contain the letter V.
2. Learn how concentration is written. Since there are different ways for expressing the "amount" of a given substance, there's more than one way to write a concentration. Here are the most common ways:^[1]
   
   • Grams per liter (g/L.) Simply the mass of a solute in grams dissolved in a given volume of solution. Usually used for solutions made from solid solutes and liquid solvents, like our sugar and vinegar example.
   • Molarity (M.) The number of moles of a solute divided by the volume of the solution. A mole is a unit often used in chemistry to describe the number of atoms or molecules of a substance.
   • Parts per million (ppm.) The number of units (usually grams or milligrams) of a solute found in one million units of the solution. Usually used for very dilute water solutions.
   • Percent composition. The number of parts (again, usually grams) of solute found in one hundred parts of solution. The percent symbol % means "out of 100" so you can easily write the fraction as a percentage.

EditCalculating Concentration as Grams per Liter

1. Understand this method. This is a useful way to measure concentration when you're dissolving a solid into a liquid, and when you're talking about solutions that involve human scale measurements. If the solute is much less than a gram or the solvent is much less than a liter, you'll probably want to use one of the other methods instead.
   
   • Example problem: Find the concentration (in grams per liter) of a solution made by dissolving 3 mL of table salt in 2000 mL of water. Write the answer in the form of grams / liter.
2. Convert the solute measurements to grams. If your solute (the substance dissolved into the larger container) is already measured in grams, skip to the next step. Otherwise, you'll need to convert it. Converting from other units of mass (such as the kilogram) should be simple if you look up the conversion rate, but converting from volume units (such as the liter) is more complicated. Each substance has a density which determines how much mass can fit into a certain volume. Look up this density and multiply it by your volume measurement to get the measurement in grams, after making sure your units match.
   
   • In our example, the salt is the solute. It is measured in a unit of volume (mL), so we'll need to convert it to grams.
   • The density of table salt is 1.15 g/mL.^[2] If this information is not included with the problem, you may need to look it up in your textbook or a database of chemical substances. We need to make sure to find the density in the units we are using (grams per mL), or convert it to the right unit.
   • To find the mass of salt in 3 mL, calculate 3 mL x (^{1.15 grams} / _{1 mL}) = 3.45 grams salt.
3. Convert the solvent measurement to liters. The solvent should just about always be measured in a unit of volume already so conversion is pretty simple. If it's already written in liters, skip to the next step.
   
   • In our example, we have 2000 mL of water. We'll need to convert this to liters.
   • There are 1000 mL per liter, so convert by calculating (^{1 L} / _{1000 mL}) x (2000 mL) = 2 liters of water.
   • Note that we arranged the conversion so that the mL units canceled out (one on top, one on bottom). If we had written it as ^{1000 mL} / _{1 L} x 2000 mL we would end up with a nonsense result.
4. Divide the solvent by the solute. Now that we have the gram measurement of the solute and the liter measurement of the solvent, calculating the g/L concentration is as easy as dividing:
   
   • In our example, ^{3.45 grams of salt} / _{2 liters of water} = 1.725 g/L salt concentration.
5. Adjust the formula for large amounts of solute. Technically, we should calculate the concentration using the volume of the entire solution, meaning the solvent and solute volumes added together. When dissolving a small amount of a solid into a large amount of liquid, this rarely makes much of a difference, so you can safely ignore the solute and just use the volume of the solvent, like we did above. If the solute volume is enough to visibly change the volume, you'll need to change the formula to (g of solute) / (L of solute + L of solvent).
   
   • In our example, ^{3.45 grams of salt} / (_{2 liters of water} + 0.003 L salt) = 1.722 g/L.
   • The difference between this and our previous answer is 0.003 g/L. This is a tiny difference, most likely smaller than the accuracy of our measurement tools.

EditCalculating Concentration as a Percentage or Parts Per Million

1. Understand the method. Use this method if you're asked to find the "percent composition" or "weight percent."^[3] In chemistry, you are most often interested in the mass of a substance. Once you know how the masses of the solute and the solvent, you can find the percentage of the solute fairly easily by comparing the two amounts.
   
   • Example problem: 10 grams of chocolate powder are dissolved in 1.2 Liters of hot water. First, calculate what percentage of the solution is chocolate. Then write the result in parts per million.
2. Convert the measurements to grams. If any measurements you are given are written in volume measurements (such as liters or milliliters), you'll need to convert them to a unit of mass: grams. Because each substance has a certain density (mass per volume), you'll need to find out the specific characteristics of the substance before you can do this:
   
   • Look up the density of the substance in your textbook or online. Convert the density so it is written in grams per (the unit of volume used in the problem), if it isn't already. Multiply the density by the volume of the substance and you'll have the mass in grams.
   • Example: You have 1.2 Liters of water. The density of water is 1000 grams per liter, so calculate (^{1000 g} / _{1 L}) x 1.2 L = 1200 grams.
   • Since our solute, the chocolate, is already measured in grams, we don't need to convert it.
3. Calculate the percent composition. Once you have the mass of the solute and the mass of the solvent, both in grams, use this formula to calculate the percent composition: (^{grams of solute (in g)} / (_{grams of solute + grams of solvent})) x 100.
   
   • We have 10 grams of chocolate, and we figured out that there are 1200 grams of water. The entire solution (solute + solvent) has a mass of 10 + 1200 = 1210 grams.
   • The concentration of the chocolate in the entire solution = ^{(10 grams chocolate)} / _{(1210 grams solution)} = 0.00826
   • Multiply this by 100 to get the percentage: 0.00826 x 100 = 0.826, so the mixture is 0.826% chocolate.
4. Calculate parts per million. Percentage is really "parts per hundred" so parts per million is calculated a very similar way. The formula is (^{grams of solute (in g)} / (_{grams of solute + grams of solvent})) x 1,000,000. In scientific notation, this is written (^{grams of solute (in g)} / (_{grams of solute + grams of solvent})) x 10⁶.
   
   • In our example, ^{(10 grams chocolate)} / _{(1210 grams solution)} = 0.00826.
   • 0.00826 x 10⁶ = 8260 parts per million chocolate.
   • Normally, parts per million is used to measure much smaller concentrations, which are less convenient to write as percentages. We're just using the same example here for convenience.

EditCalculating Molarity

1. Know what you need for this method. Molarity requires you to know how many moles there are of your solute, but these can be easily derived if you know the mass of your solute and its chemical formula. If you do not have all this information, or if you've never been taught the concept of "mole" in a chemistry context, use a different method instead.
   
   • Example problem: What is the molarity of a solution created by dissolving 25 grams of potassium hydroxide in 400 mL of water?
   • If the solute is measured in units other than grams, you'll need to convert to grams first.
2. Calculate the molar mass of the solute. Each chemical element has a known "molar mass" (MM), which is the mass contained in one mole of that element. These molar masses have the same value as the atomic mass displayed on the periodic table, generally under the chemical symbol and name of each element. Simply add the molar masses of the solute's component elements to figure out the solute's molar mass.
   
   • Our example uses potassium hydroxide as the solute. Look this substance up in your textbook or in an online chemical formula database to find the chemical formula: KOH.
   • Use a periodic table or online resource to find the atomic mass of the element: K = 39.0, O = 16.0, H = 1.0.
   • Add the atomic masses together and write "g/mol" after it to get the molar mass. 39 + 16 + 1 = 56 g/mol.
   • If we had a molecule with more than one of the same atom, add the atomic mass once for each atom. For example, H₂O has a molar mass of 1 + 1 + 16 = 18 g/mol.
3. Calculate the amount of solute in moles. Once you have the molar mass (g/mol), you can convert between grams and moles. You already know the amount of solutes in grams, so convert by calculating (solute mass in grams) x (¹ / _{molar mass}) to get the answer in moles.
   
   • In our example, since we have 25 grams of a substance with a molar mass of 56 g/mol, we calculate 25g x (¹ / _56g/mol) = approximately 0.45 moles KOH in our solution.
4. Divide by the liter measurement of the solution to find the molarity. Molarity is defined as the ratio of moles of the solute to liters of the solution. Convert the solution's volume measurement to liters if necessary, then do the calculation.
   
   • In our example, we have 400 mL of water, which we can convert to 0.4 liters.
   • The molarity of the KOH in the solution is ^{0.45 mol} / _0.4L = 1.125 M (molarity). (You'll get a slightly more accurate answer if you use a calculator and don't round any numbers until the final step.)
   • You can usually disregard the volume of the solute, since it rarely makes a big difference. If you are adding enough solute to visibly change the volume, measure the volume of the final solution and use that instead.

EditPerforming Titrations to Calculate Concentration

1. Know when a titration is appropriate. A titration is a technique used by chemists to calculate the amount of solute present in a solution. To perform a titration, you create a chemical reaction between your solute and another reactant (usually also dissolved in a liquid solution.) Because you know the precise amount of your second reactant and you know the chemical equation for the reaction between it and your solute, you can calculate the amount of your solute by measuring how much reactant you need to add before the reaction with your solute completes.
   
   • Thus, titrations can be very useful for calculating the concentration of a solution when you don't know how much solute was initially added.
   • If you already know how much solute is in the solution, you don't need to titrate - simply measure the volume of your solution and calculate concentration as in Part One.
2. Set up your titration equipment. Accurate titrations require clean, precise, professional-grade chemical equipment. Set up a titration area with an Erlenmeyer flask or beaker underneath a calibrated burette affixed to a burette stand. The tip of the burette should be in the neck of the flask or beaker without touching any sides.
   
   • Make sure all equipment has been previously cleaned, rinsed with deionized water, and allowed to dry.
3. Fill your flask and burette. Precisely measure a small quantity of your unknown-concentration solution. When your solute dissolves, it spreads evenly throughout the solution, so the concentration of this small sample will be the same as the original solution. Fill your burette with a solution of known concentration that will react with your solution. Record the exact volume of the solution in the burette - you will subtract the final volume to find the total solution used in the reaction.
   
   • Note: if the reaction between the solution in the burette and the solute of unknown concentration in the flask doesn't show any visual signs of reaction, you'll need to add an indicator to your flask. In chemistry, indicators are chemicals that give a visual a solution when a reaction reaches its equivalence point or end point. Indicators are commonly used for titrations involving acid-base and redox reactions, but a wide variety of other indicators exist. Consult a chemistry textbook or an online guide to find an appropriate indicator for your reaction.
4. Begin the titration. Gradually add solution from the burette (called "titrant") to the flask. Use a magnetic stirrer or a glass rod to gently mix the solutions as they react. If your solutions react visibly, you should see signs of their reaction - color change, bubbles, products formed, etc. If you're using an indicator, you may still see flashes of color as each drop from the burette enters the flask.
   
   • If your reaction results in a change in pH or potential, you can insert pH readers or potentiometers into the flask to monitor the reaction's progress.
   • For a more precise titration, monitor the pH or potential as above, recording the reading after adding small set amounts of titrant. Graph your solution's pH or potential against the volume of titrant added. You'll get sharp changes in the slope of the curve at the reaction's equivalence points.
5. Slow your titration. As your reaction approaches its endpoint, slow your titration to a drop-by-drop pace. If you're using an indicator, you may notice the flashes of color it gives are persisting for longer. Proceed as slowly as possible until you reach the exact drop that causes your reaction to reach its endpoint. For indicators, you will generally look for the earliest possible persistent color change in your reaction.
   
   • Record the final volume in your burette. By subtracting this from your initial burette volume, you can find the precise volume of titrant you used.
6. Calculate the amount of solute in your solution. Use the chemical equation for the reactant between your titrant and your solution to find the moles of solute in your flask. Once you've found the moles of solute, you can simply divide by the volume of solution in the flask to find the molarity of the solution, or convert moles to grams and divide by the volume of the solution to find the concentration in g/L. This will require a basic understanding of Stoichiometry.
   
   • For example, let's say that we used 25 mL of .5 M NaOH to titrate a solution of HCl and water to its equivalence point. The HCl solution had a volume of 60 mL before titration. How many moles of HCl are in our solution?
   • To start, let's look at the chemical equation for the reaction of NaOH and HCl: NaOH + HCl > H₂O + NaCl
   • In this case, one molecule of NaOH reacts with one molecule of HCl to create the products (water and NaCl.) So, since you added just enough NaOH to neutralize all of the HCl, the number of moles of NaOH consumed in the reaction will equal the number of moles of HCl in the flask.
   • So, let's find the amount of NaOH in moles. 25 mL NaOH = .025 L NaOH x (.5 moles NaOH/1 L) = .0125 moles NaOH.
   • Since we deduced from the reaction equation that the moles of NaOH consumed = the moles of HCl in the solution, we know that we have .0125 moles HCl in solution.
7. Calculate your solution's concentration. Now that you know the amount of solute in your solution, it's easy to find your concentration in terms of molarity. Simply divide the moles of solute in your solution by the volume of your solution sample (not the volume of the larger source you took your sample from.) The result is the molarity of your solution!
   
   • To find molarity for our example above, simply divide the moles of HCl by the volume in the flask. .0125 moles HCl x (1/.060 L) = .208 M HCl.
   • To convert molarity to g/L, ppm, or percent composition, you'll need to convert the moles of your solute to a mass (using the molar mass of your solute compound.) For ppm and percent composition, you'll also need to convert the volume of your solution to a mass (using a conversion factor such as density or by simply weighing it.), then multiply the result by 10⁶ or 10², respectively.

EditTips

• Though the solute and solvent can be different states of matter (solid, liquid, or gas) when separate, the solution formed when the solvent dissolves the solute is the same state of matter as the solvent.
• Use clear plastic or glassware only for titration.

EditWarnings

• Wear goggles and gloves during titration.
• Be careful when working with any strong acid. Work under a fume hood, or outside in the fresh air.

EditRelated wikiHows

• How to Calculate Molar Mass
• How to Lower Ammonia Levels in Your Fish Tank
• How to Control an Algae Bloom
• How to Reduce Saltwater Reef Aquarium Maintenance

EditSources and Citations

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