In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation. To define a solution precisely, we need to state its concentration: how much solute is dissolved in a certain amount of solvent. Words such as dilute or concentrated are used to describe solutions that have a little or a lot of dissolved solute, respectively, but these are relative terms with meanings that depend on various factors. Concentration is the measure of how much of a given substance is mixed with another substance. Solutions are said to be either dilute or concentrated. When we say that vinegar is \(5\%\) acetic acid in water, we are giving the concentration. If we said the mixture was \(10\%\) acetic acid, this would be more concentrated than the vinegar solution. A concentrated solution is one in which there is a large amount of solute in a given amount of solvent. A dilute solution is one in which there is a small amount of solute in a given amount of solvent. A dilute solution is a concentrated solution that has been, in essence, watered down. Think of the frozen juice containers you buy in the grocery store. To make juice, you have to mix the frozen juice concentrate from inside these containers with three or four times the container size full of water. Therefore, you are diluting the concentrated juice. In terms of solute and solvent, the concentrated solution has a lot of solute versus the dilute solution that would have a smaller amount of solute. The terms "concentrated" and "dilute" provide qualitative methods of describing concentration. Although qualitative observations are necessary and have their place in every part of science, including chemistry, we have seen throughout our study of science that there is a definite need for quantitative measurements in science. This is particularly true in solution chemistry. In this section, we will explore some quantitative methods of expressing solution concentration.
There are several ways of expressing the concentration of a solution by using a percentage. The mass/mass percent (% m/m) is defined as the mass of a solute divided by the mass of a solution times 100: \[\mathrm{\% \:m/m = \dfrac{mass\: of\: solute}{mass\: of\: solution}\times100\%} \nonumber \] mass of solution = mass of solute + mass solvent If you can measure the masses of the solute and the solution, determining the mass/mass percent is easy. Each mass must be expressed in the same units to determine the proper concentration. Suppose that a solution was prepared by dissolving \(25.0 \: \text{g}\) of sugar into \(100.0 \: \text{g}\) of water.
mass of solution = 25.0g sugar + 100.0g water = 125.0 g
\[\text{Percent by mass} = \dfrac{25.0 \: \text{g sugar}}{125.0 \: \text{g solution}} \times 100\% = 20.0\% \: \text{sugar} \nonumber \]
A saline solution with a mass of 355 g has 36.5 g of NaCl dissolved in it. What is the mass/mass percent concentration of the solution?
We can substitute the quantities given in the equation for mass/mass percent: \(\mathrm{\%\: m/m=\dfrac{36.5\: g}{355\: g}\times100\%=10.3\%}\)
A dextrose (also called D-glucose, C6H12O6) solution with a mass of 2.00 × 102 g has 15.8 g of dextrose dissolved in it. What is the mass/mass percent concentration of the solution? Answer7.90 %
Sometimes you may want to make up a particular mass of solution of a given percent by mass and need to calculate what mass of the solute to use. Using mass percent as a conversion can be useful in this type of problem. The mass percent can be expressed as a conversion factor in the form \(\dfrac{g \; \rm{solute}}{100 \; \rm{g solution}}\) or \(\dfrac{100 \; \rm g solution}{g\; \rm{solute}}\) For example, if you need to make \(3000.0 \: \text{g}\) of a \(5.00\%\) solution of sodium chloride, the mass of solute needs to be determined.
Given: 3000.0 g NaCl solution 5.00% NaCl solution Find: mass of solute = ? g NaCl Other known quantities: 5.00 g NaCl is to 100 g solution
To solve for the mass of NaCl, the given mass of solution is multiplied by the conversion factor. \[g NaCl = 3,000.0 \cancel{g \: NaCl \:solution} \times \dfrac{5.00 \:g \: NaCl}{100\cancel{g \: NaCl \: solution}} = 150.0g \: NaCl \nonumber \] You would need to weigh out \(150 \: \text{g}\) of \(\ce{NaCl}\) and add it to \(2850 \: \text{g}\) of water. Notice that it was necessary to subtract the mass of the \(\ce{NaCl}\) \(\left( 150 \: \text{g} \right)\) from the mass of solution \(\left( 3000 \: \text{g} \right)\) to calculate the mass of the water that would need to be added.
What is the amount (in g) of hydrogen peroxide (H2O2) needed to make a 6.00 kg, 3.00 % (by mass) H2O2 solution? Contributors and Attributions LICENSED UNDER
The percentage concentration of any solution is most commonly expressed as mass percent: Mass % of any component of the solution = Other methods are: Volume % of a component = i.e. Mass by Volume percentage = Here's a point to be kept in mind : The concentration of a solution is most of the time expressed as the number of moles of solute present in 1 Liter of the solution (also called molarity ) (There are also other ways to express concentration. Please follow this link. ) EXAMPLE: (b) What is the molarity of a solution prepared by dissolving 15.0 g of sodium hydroxide in enough water to make a total of 225 mL of solution? Solution Moles of NaOH = 15.0 g NaOH × #(1"mol NaOH")/(40.00"g NaOH")# = 0.375 mol NaOH Volume = 225 mL × #(1"L")/(1000"mL")# = 0.225 L soln Molarity = #(0.375"mol")/(0.225"L")# = 1.67 mol/L
Let's address the question for both percent concentration by mass and for percent concentration by volume. Percent concentration by mass is defined as the mass of solute divided by the total mass of the solution and multiplied by 100%. So, #c% = m_(solute)/(m_(solution)) * 100%#, where #m_(solution) = m_(solvent) + m_(solute)# There are two ways to change a solution's concentration by mass
Let's take an example to better illustrate this concept. Say we dissolve 10.0g of a substance in 100.0g of water. Our concentration by mass will be #c% = (10.0g)/(10.0g + 100.0g) * 100% = 9.09%# Now let's try doubling the mass of the solute; the new concentration will be #c% = (2 * 10.0g)/(2*10.0g + 100.0g) * 100% = 16.7%# However, if we keep the mass of the solute at 10.0g and doubled the mass of the solvent (in this case, water), the concentration will be #c% = (10.0g)/(10.0g + 2*100.0g) * 100% = 4.76%# The same is true for percent concentration by volume, which is defined as the volume of the solute divided by the total volume of the solution and multiplied by 100%. #c_(volume)% = V_(solute)/(V_(solute) + V_(solvent)) * 100%# It's easy to see that manipulating either the volume of the solute or the volume of the solvent (or both) would change the solution's percent concentration by volume.
There are two types of percent concentration: percent by mass and percent by volume. PERCENT BY MASS Percent by mass (m/m) is the mass of solute divided by the total mass of the solution, multiplied by 100 %. Percent by mass = #"mass of solute"/"total mass of solution"# × 100 % Example What is the percent by mass of a solution that contains 26.5 g of glucose in 500 g of solution? Solution Percent by mass = #"mass of glucose"/"total mass of solution" × 100 % = (26.5"g")/(500"g")# × 100 % = 5.30 % PERCENT BY VOLUME Percent by volume (v/v) is the volume of solute divided by the total volume of the solution, multiplied by 100 %. Percent by volume = #"volume of solute"/"total volume of solution"# × 100 % Example How would you prepare 250 mL of 70 % (v/v) of rubbing alcohol Solution 70 % = #"volume of rubbing alcohol"/"total volume of solution" × 100 %# × 100 % So Volume of rubbing alcohol = volume of solution × #"70 %"/"100 %"# = 250 mL × #70/100# = 175 mL You would add enough water to 175 mL of rubbing alcohol to make a total of 250 mL of solution.
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What is the concentration of a solution in by mass if it contains 35g of sugar in 175g of a solution
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