what is the mass percent of nacl in a solution that is prepared by adding 76.0 g nacl to 113 g water

thirteen.five: Solution Concentration: Mass Percent

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105380

Learning Objectives

• Express the amount of solute in a solution in various concentration units.

To define a solution precisely, we need to country 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 accept a little or a lot of dissolved solute, respectively, merely these are relative terms whose meanings depend on various factors.

Introduction

Concentration is the measure of how much of a given substance is mixed with another substance. Solutions can exist said to be dilute or concentrated. When we say that vinegar is \(v\%\) acetic acid in h2o, nosotros are giving the concentration. If we said the mixture was \(10\%\) acetic acrid, this would be more full-bodied than the vinegar solution.

Figure \(\PageIndex{ane}\): The solution on the left is more full-bodied than the solution on the right because in that location is a greater ratio of solute (red balls) to solvent (blue balls) particles. The solution particles are closer together. The solution on the correct is more than dilute (less concentrated). (CC-SA-By-3.0 Tracy Poulsen).

A concentrated solution is one in which there is a large amount of solute in a given amount of solvent. A dilute solution is 1 in which there is a minor corporeality of solute in a given amount of solvent. A dilute solution is a concentrated solution that has been, in essence, watered downwards. Retrieve of the frozen juice containers you buy in the grocery shop. What yous have to practice is take the frozen juice from within these containers and ordinarily empty it into 3 or 4 times the container size full of h2o to mix with the juice concentrate and make your container of juice. Therefore, you lot are diluting the concentrated juice. When we talk nigh 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 accept their place in every part of science, including chemical science, we accept seen throughout our study of science that in that location is a definite need for quantitative measurements in scientific discipline. This is particularly true in solution chemistry. In this department, we will explore some quantitative methods of expressing solution concentration.

Mass Percent

There are several ways of expressing the concentration of a solution by using a percent. The mass/mass percent (% m/m) is defined as the mass of a solute divided by the mass of a solution times 100:

\[\mathrm{\% \:1000/grand = \dfrac{mass\: of\: solute}{mass\: of\: solution}\times100\%}\]

mass of solution = mass of solute + mass solvent

If you can measure the masses of the solute and the solution, determining the mass/mass per centum is easy. Each mass must exist expressed in the same units to determine the proper concentration.

Suppose that a solution was prepared past dissolving \(25.0 \: \text{k}\) of carbohydrate into \(100.0 \: \text{g}\) of water.

The mass of the solution is

mass of solution = 25.0g sugar + 100.0g water = 125.0 g

The percentage past mass would be calculated by:

\[\text{Percent by mass} = \frac{25.0 \: \text{g saccharide}}{125.0 \: \text{g solution}} \times 100\% = 20.0\% \: \text{sugar}\]

Case \(\PageIndex{1}\)

A saline solution with a mass of 355 g has 36.five m of NaCl dissolved in it. What is the mass/mass percent concentration of the solution?

Solution

Nosotros tin substitute the quantities given in the equation for mass/mass per centum:

\(\mathrm{\%\: 1000/yard=\dfrac{36.5\: g}{355\: g}\times100\%=10.iii\%}\)

Do \(\PageIndex{1}\)

A dextrose (too called D-glucose, C₆H₁₂O₆) solution with a mass of two.00 × ten² grand has xv.8 grand of dextrose dissolved in it. What is the mass/mass percentage concentration of the solution?

Reply

7.xc %

Using Mass Percent in Calculations

Sometimes you may desire to brand upward a particular mass of solution of a given percent by mass and need to summate what mass of the solute to utilise. Using mass percent equally a conversion tin can be useful in this type of problem. The mass percentage tin be expressed as a conversion factor in the form \(\frac{g \; \rm{solute}}{100 \; \rm{g solution}}\) or \(\frac{100 \; \rm g solution}{g\; \rm{solute}}\)

For example, if you need to make \(3000.0 \: \text{g}\) of a \(five.00\%\) solution of sodium chloride, the mass of solute needs to be adamant.

Solution

Given: 3000.0 m NaCl solution

five.00% NaCl solution

Discover: mass of solute = ? 1000 NaCl

Other known quantities: 5.00 k NaCl is to 100 yard solution

The appropriate conversion cistron (based on the given mass percent ) can be used follows:

To solve for the mass of NaCl, the given mass of solution is multiplied by the conversion factor.

\[thousand NaCl = 3,000.0 \cancel{g \: NaCl \:solution} \times \frac{v.00 \:1000 \: NaCl}{100\cancel{g \: NaCl \: solution}} = 150.0g \: NaCl\]

Y'all would demand to weigh out \(150 \: \text{g}\) of \(\ce{NaCl}\) and add together information technology to \(2850 \: \text{g}\) of water. Discover 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.

Practice \(\PageIndex{i}\)

What is the amount (in g) of hydrogen peroxide (H ₂ O ₂ ) needed to make a vi.00 kg , 3.00 % (past mass) H ₂ O _two solution?

Answer

180. g H ₂ O _two

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Source: https://chem.libretexts.org/Courses/Palomar_College/PC%3A_CHEM100_-_Fundamentals_of_Chemistry/13%3A_Solutions/13.05%3A_Specifying_Solution_Concentration%3A_Mass_Percent