Molarity - Online Tutor, Practice Problems & Exam Prep

Understanding the concept of molarity is crucial for solving problems in chemistry. Molarity, denoted by the symbol M, is a measure of concentration that indicates the number of moles of solute per liter of solution. The formula for molarity is:

$M=\frac{\mathrm{moles}\mathrm{of}\mathrm{solute}}{\mathrm{liters}\mathrm{of}\mathrm{solution}}$

This formula serves as a conversion factor in calculations, allowing us to find unknown quantities in a solution. For instance, a solution with a molarity of 5.8 M sodium chloride means it contains 5.8 moles of NaCl in one liter of solution. When performing calculations involving molarity, it's important to recognize that molarity can be used to convert between moles of solute and volume of solution, facilitating the determination of various components within a chemical solution.

Molarity

In these series of videos, we're going to take a look at the concept of molarity. Now molarity itself is represented by the variable M and in class you'll hear molarity and concentration sometimes being used interchangeably. Remember, concentration represents the amount of given solute within a certain amount of solution.

Now molarity is more specific. Molarity represents the number of moles of solute per liter of solution and with this we have our molarity formula. So molarity which is capital M equals moles of solute over liters of solution.

Now that we have a more fleshed out idea of what concentration is through molarity, let's take a look at some problems or asked to calculate molarity, or to look at the components that help to make molarity.

M = moles   of   solute liters   of   solution

Molarity Example 1

Here it says to calculate the molarity of a solution prepared by dissolving two 3.7 grams of sodium hydroxide in enough water to make 2.50 liters of solution. So here we're looking for molarity. So molarity here equals our moles of solute, which would be the NaOH. And it is. And it's in a solution of 2.50 liters. So we need liters of solution.

All right, we already have the 2.50 liters of solution, so we just need to convert the grams of sodium hydroxide into moles. So one mole of sodium hydroxide goes on the bottom, and then grams of sodium hydroxide go. One mole goes on the top and grams of sodium hydroxide go on the bottom. Sodium hydroxide is composed of one sodium, one oxygen and one hydrogen. Multiply them by their atomic masses from the periodic table and then add up the totals. This will give us the molar mass of sodium hydroxide.

So when we add that all up, it's 39.998 grams. So that's going to go here. So here grams of sodium hydroxide cancel out and now I'm going to have moles of sodium hydroxide. So that comes out to 0.5925 moles. Take that and plug it in and we'll have the molarity of our solution. So this comes out to 0.237 molar for our solution.

Molarity

Now that we know what Molarity is, we can use it to help us calculate unknowns. We're going to say problems with a molarity value present can use a given amount and conversion factors to isolate and end amount. Now if you haven't watched our videos on dimensional analysis and conversion factors, I highly suggest you go back and take a look because it's just a continuation of this.

We're now incorporating Molarity into our calculations. Now the Molarity value itself can represent one of those conversion factors, because remember conversion factors possess two different units connected together. Now for example, we say 5.8 molar sodium chloride. 5.8 molar represents 5.8 moles of NaCl within one liter of solution.

And because we're using two different units connected together, this is a conversion factor. So we can write it as 5.8moles of NaCl 1liter of solution. So this is what 5.8 molar really represents. So keep that in mind when we start doing calculations that incorporate molarity.

Molarity Example 2

In this example question, it says how many grams of sodium phosphate, which has a molecular mass of 163.94 grams per mole, are present in 300 milliliters of a .550 molar sodium phosphate solution. All right, so in this question they're asking us to discover grams. Now, before we start plugging in numbers and doing calculations, let's talk about what the sentence is saying and how we need to be on the look at when we see it written in such a way.

Now here we have a number and here we have another number and they are connected together by the word of. So just remember when of is in between two values of is really telling us to multiply them together. Now we have molarity here which remember molarity equals moles over liters and realize this that if I were to multiply both sides by liters then we would see that moles equals liters times molarity. Look at this, this is milliliters. If I were to convert those into liters and then multiply it by the molarity, that would give me moles of sodium phosphate.

And we know if we have moles of a compound, we can use its molecular mass or molar weight to help us determine the grams of that compound. So that's the key. So just remember here when we have volume of molarity, that's really just telling us, hey you have moles there, all right. So we're going to first take the 300 milliliters and I'm going to convert it into liters. Remember this is a metric prefix conversion, so milliliters go on the bottom, liters go on top. Remember that the metric prefix is on the same side with one, so 1,000,000 is 10 to the -3 milliliters cancel out. Now I have liters.

Also remember that molarity is a conversion factor, so that .550 molar is really saying that I have 0.550 moles of that compound over one liter, so I need liters to cancel out. So I'll put the one liter here and then we have 0.550 moles of sodium phosphate here. Liters cancel out and look, I have moles of sodium phosphate. Finally, I convert those moles into grams. So one mole of sodium phosphate. We're told that the molecular weight is 163.94 grams. So plug that in so moles cancel out and I'll be left with grams at the end.

So initially what I'll get is 27.0501 grams of sodium phosphate. Looking at the question, 300.0 has four sig figs, .550 has three sig figs, and this number here has five sig figs. We go with the least number of significant figures, so this comes out to be 27.1g of sodium phosphate. So this would be the grams of our compound. So just remember, when they're giving us volume of molarity, they're telling us what the moles are here. In this case, we just had to find grams. So take those moles that you've isolated and convert them into grams and you'll have your final answer.

What volume in (µL) of 0.125 M HBr contains 0.170 moles HBr?

• A. 7.35x10³ μ L
• B. 7.35x10⁶ μ L
• C. 1.36x10³ μ L
• D. 1.36x10⁹ μ L
• E. 1.36x10⁶ μ L

Hypernatremia is a medical condition where a patient has high levels of sodium in their blood, and is the result of the body containing too little water. A patient has a measured sodium level of 165 mM. If 30.0 mL of their blood were drawn, what mass (in ng) of sodium would be present?

• A. 1.14x10⁷ ng
• B. 1.14x10⁶ ng
• C. 1.14x10⁸ ng
• D. 4.18x10⁸ ng
• E. 4.18x10⁶ ng

2.64 grams of an unknown compound was dissolved in water to yield 150 mL of solution. The concentration of the solution was 0.075 M. What was the molecular weight of the substance?

• A. 190 g/mol
• B. 30 g/mol
• C. 90 g/mol
• D. 240 g/mol
• E. 320 g/mol

A solution with a final volume of 750.0 mL was prepared by dissolving 30.00 mL of benzene (C₆H₆, density = 0.8787 g/mL) in dichloromethane. Calculate the molarity of benzene in the solution.

• A. 0.45 M
• B. 0.035 M
• C. 0.35 M
• D. 0.71 M
• E. 0.091 M

Here’s what students ask on this topic:

How do you calculate molarity?

Molarity is a measure of the concentration of a solute in a solution. To calculate molarity, you follow these steps:

1. Identify the number of moles of solute present. To find the moles, you can use the formula: $\mathrm{moles}=\frac{\mathrm{mass}\left(\mathrm{in\; grams}\right)}{\mathrm{molar\; mass}}$ (the molar mass is the mass of one mole of the substance, which can be found on the periodic table or a chemical database).
2. Measure the volume of the solution in liters. If the volume is given in milliliters or another unit, convert it to liters by dividing by 1000 (since there are 1000 milliliters in one liter).
3. Divide the number of moles of solute by the volume of the solution in liters. The resulting value is the molarity of the solution.

The formula for molarity (M) is:

$M=\frac{\mathrm{moles\; of\; solute}}{\mathrm{liters\; of\; solution}}$

For example, if you dissolve 0.5 moles of sodium chloride (NaCl) in enough water to make 1 liter of solution, the molarity of the NaCl solution is 0.5 M (0.5 moles / 1 L = 0.5 M).

What is molarity?

Molarity is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute dissolved in one liter of solution. The moles of a substance are a measure of the number of particles, such as atoms, ions, or molecules, it contains, and this is based on the substance's molecular weight. Molarity is expressed in units of moles per liter (mol/L).

To calculate molarity, you can use the formula:

$M=\frac{\mathrm{moles} \mathrm{of} \mathrm{solute}}{\mathrm{liters} \mathrm{of} \mathrm{solution}}$

For example, if you dissolve 1 mole of sodium chloride (NaCl) in 1 liter of water, the molarity of the resulting solution is 1 M. If you dissolve 0.5 moles of NaCl in the same volume of water, the molarity is 0.5 M. Molarity is a convenient way to express concentration because it directly relates to the volume of solution, making it useful for stoichiometry in chemical reactions where volume measurements are commonly performed.

How do you find moles from molarity?

To find the number of moles from molarity, you need to know two things: the molarity of the solution and the volume of the solution in liters. Molarity (M) is defined as the number of moles of solute (the substance being dissolved) per liter of solution.

Here's the formula you'll use:

$\text{Number of Moles}=\text{Molarity (M)}\times \text{Volume (L)}$

For example, if you have a solution with a molarity of 2 M and you have 3 liters of this solution, you would calculate the number of moles of solute as follows:

$\text{Number of Moles}=2\text{M}\times 3\text{L}=6\text{moles}$

So, in this example, there are 6 moles of the solute in 3 liters of the 2 M solution. Remember to always ensure that the volume is in liters when using this formula, as molarity is defined in terms of moles per liter. If you have volume in milliliters or another unit, you'll need to convert it to liters first (1 L = 1000 mL).

What are the units for molarity?

Molarity is a measure of the concentration of a solute in a solution. It is expressed in units of moles per liter (mol/L). In other words, molarity describes how many moles of a substance are present in one liter of solution. To calculate molarity, you divide the number of moles of the solute by the volume of the solution in liters. It's a commonly used unit in chemistry for quantifying the concentration of substances in a given volume of liquid, and it's particularly useful for reactions that take place in solution. Remember that when you're preparing solutions in a lab, it's important to measure volumes accurately to ensure that the resulting molarity is as intended for your experiments or calculations.

How can moles be found using molarity and volume?

To find the number of moles using molarity and volume, you can use the following formula:

$\mathrm{Moles}=\mathrm{Molarity}\left(M\right)\times \mathrm{Volume}\left(L\right)$

Here's how it works:

1. Molarity (M) is the concentration of a solution expressed as the number of moles of solute per liter of solution. It tells you how many moles of a substance are in one liter of the solution.

2. Volume (L) is the amount of the solution you have, measured in liters. If your volume is given in milliliters (mL) or another unit, you'll need to convert it to liters by dividing by 1000 (since 1000 mL = 1 L).

3. Multiply the molarity by the volume in liters to find the number of moles of solute in your solution.

For example, if you have 2 liters of a 0.5 M NaCl solution, you would calculate the moles of NaCl as follows:

$\mathrm{Moles}=0.5\times 2L=1\mathrm{mole}\mathrm{of}\mathrm{NaCl}$

This means there is 1 mole of NaCl dissolved in the 2 liters of solution.