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Find the Concentration of a Solution With Density



The Volumetric Flask


Molarity
Molarity is defined to be:


Molarity is probably the most commonly employed of all solution concentration units. This is due to the utility of the volumetric flask in the laboratory. Volumetric flasks are specifically calibrated for a variety of solution volumes (among the most common specific volumes are: 5 L, 2 L, 1 L, 750 mL, 500 mL, 250 mL 100 mL, 50 mL 25 mL and 10 mL). To prepare a solution of the proper molarity, one weighs out the appropriate mass of solute to produce the correct number of moles, transfers it to the volumetric flask, fills the flask to the base of the neck, dissolves the solute, then fills the flask to the calibration mark etched in the neck. For calculation purposes, we will assume our volumetric flasks provide a volume accurate to ± 0.1 mL.

Sample Calculations using Molarity

  1. 25.00 grams of solute NaCl (molar mass = 58.44 g/mole) is dissolved in a 250 mL volumetric flask. What is the molarity of this solution?

  2. How many grams of sucrose (C12H22O11 , molar mass = 342.3 g/mole) are required to make 500 mL of a solution that is 0.1500 M?

  3. How many mL total volume of solution must be produced to make a 0.220 M solution using 1.00 g of the solute LiF (molar mass = 25.94 g/mole)?

  4. 25.0 mL of a 0.125 M solution of KCl is mixed with 15.0 mL of a 0.440 M solution of KCl, then an additional 20.0 mL of water is added. What is the final molarity of the solution?




Practice Problems:
  1. How many grams of sucrose (molar mass = 342.3 g/mole) are required to make 125 mL of solution which is 0.150 M? (Answer: 6.42 g)
  2. 42.0 g of solute KCl (molar mass = 113.7 g/mole) is placed into 100 mL total solution. What is the molarity? (Answer: 3.69 M)
  3. 20.0 mL of 1.00 M LiF is added to 15.0 mL of 1.50 M LiF, then an additional 50.0 mL of water is added. What is the molarity of the final solution? (Answer: 0.500 M)
  4. What volume of total solution must be made to make 1.70 g of NaCl (molar mass = 58.44 g/mole) into a 0.250 M solution? (answer: 116 mL)
  5. 10.0 mL of 0.500 M sucrose is mixed with 25.0 mL of water. What is the final molarity of the solution? (Answer: 0.143 M)
  6. What is the molarity of a solution formed by mixing 15.0 g of LiF (molar mass = 25.94 g/mole) into 250 mL of solution? (Answer: 2.31 M)
  7. What volume of total solution must be made to mix 20.0 g of sucrose (molar mass = 342.3 g/mole) into a 1.00 M solution? (Answer: 58.4 mL)
  8. How many grams of NaCl (molar mass = 58.44 g/mole) are required to make 100 mL of a 1.75 M solution? (Answer: 10.2 g)

Molality
Molality is defined to be:

Although this definition is similar to that used for molarity, there is an important distinction to the denominator. Firstly, the definition of molality includes only the solvent in its denominator, as opposed to molarity which includes the entire solution. Secondly, the definition of molality has the mass of solvent in its denominator, as opposed to the molarity's volume of solution. Because mass units are independent of temperature, molality units are also independent of temperature. Since molarity units include volume, and volume is temperature-dependent, molarity varies with temperature. As temperature increases, molarity decreases, and as temperature decreases, molarity increases.

Sample Calculations Using Molality

  1. 1.00 g of sucrose (molar mass = 342.3 g/mole) is added to 15.0 g of water. What is the molality of solution?

  2. How many grams of sucrose (molar mass = 342.3 g/mole must be added to 115 g of water to make a solution that is 1.50 molal?

  3. A solution of NaCl (molar mass = 58.44 g/mole) with molarity = 1.25 M has a density of 1.08 g/mL. What is its molality?
    One Liter of solution contains 1.25 mole of NaCl



  4. A solution of sucrose (molar mass = 342.3 g/mole) has density 1.10 g/mL and a molality of 0.880 m. What is its molarity?
    One kg of solution contains 0.880 mole of sucrose




Practice Problems:

  1. How many grams of LiF (molar mass = 25.94 g/mole) does it take to add to 100 g of water to make a 0.100 m solution? (Answer: 0.259 g)
  2. What is the molality when 15.0 g of sucrose (molar mass = 342.3 g/mole) is added to 425 g of water? (Answer: 0.103 m)
  3. A 1.00 m solution of KCl (molar mass = 74.55 g/mole) has a density of 1.05 g/mL. What is its molarity? (Answer: 0.977 M)
  4. A 0.450 M solution of KI (molar mass = 166.0 g/mole) has a density of 1.10 g/mL. What is its molality? (Answer: 0.439 m)
  5. What mass of water in grams must be added to 22.0 g of sucrose (molar mass = 342.3 g/mole) to make a solution which has molality of 0.500? (Answer: 129 g)
  6. A 0.750 M solution of ethanol (molar mass = 46.0 g/mole) has density 0.900 g/mL. What is is its molality? (Answer: 0.867 m)
  7. How many grams of NaCl (molar mass = 58.44 g/mole) must be added to 5.50 g of water to make a solution that has molality of 0.350? (Answer: 0.112 g)
  8. A 1.75 m solution of ethanol (molar mass = 46.0 g/mole) has density 0.850 g/mL. What is its molarity? (Answer: 1.38 M)

Mole Fraction

The mole fraction is defined to be:

The above is for a binary, or two-component, system. For a mixture of three components a, b, and c:
Note that the sum of mole fractions is always unity, such as for a two-component system:

Sample Calculations Using Mole Fraction:
  1. 15.0 g of water (molar mass = 18.0 g/mole) is mixed with 15.0 g of ethanol (molar mass = 46.0 g/mole). What is the mole fraction of each component?



  2. How many grams of sucrose (molar mass = 342.3 g/mole must be added to 25.0 g of water (molar mass = 18.0 g/mole) to make a solution which has Xsucrose = 0.100?





  3. What is the mole fraction of solute in a 0.450 m solution of NaCl (molar mass = 58.44 g/mole) in water (molar mass = 18.0 g/mole)?
    One kg of solvent contains 0.450 moles of NaCl

  4. How many grams of water (molar mass = 18.0 g/mole) must be added to 10.0 g of NaCl (molar mass = 58.44 g/mole) to make a solution which has XNaCl = 0.0850?




Practice Problems:
  1. What is the mole fraction of each component when 20.0 g of sucrose (molar mass = 342.3 g/mole) is mixed with 20.0 g of water (molar mass = 18.0 g/mole)? (Answer: Xsucrose = 0.0500 Xwater = 0.950)
  2. What is the mole fraction of a 1.50 m solution of NaCl in water (molar mass = 18.0 g/mole)? (Answer: XNaCl = 0.0263 Xwater = 0.974)
  3. How many grams of water (molar mass = 18.0 g/mole) must be added to 25.0 g of sucrose (molar mass = 342.3 g/mole) to make a solution that has Xsucrose = 0.100? (Answer: 11.8 g)
  4. How many grams of LiF (molar mass = 25.94 g/mole) must be added to 15.0 g of water (molar mass = 18.0 g/mole) to make a solution which has XLiF = 0.250? (Answer: 7.23 g)
  5. What is the mole fraction of a 0.200 m solution of KI in water (molar mass = 18.0 g/mole)? (Answer: XKI = 0.00448)
  6. What is the mole fraction when 30.0 g of KCl (molar mass = 74.55 g/mole) is added to 50.0 g of water (molar mass = 18.0 g/mole)? (Answer: XKCl = 0.126 Xwater = 0.874)
  7. How many grams of NaCl (molar mass = 58.44 g/mole) must be added to 12.0 g of water (molar mass = 18.0 g/mole) to make a solution which has XNaCl = 0.0500? (Answer: 0.205 g)
  8. How many grams of water (molar mass = 18.0 g/mole) must be added to 5.00 g of ethanol (molar mass = 46.0 g/mole) to make a solution which has Xethanol = 0.750? (Answer: 0.648 g)

Percent by Mass The percent by mass of component A of a binary mixture is defined to be:

This definition applies to any multi-component solution by including the mass of each component in the total mass of the denominator. Percent mass is a dimensionless quantity reported as a percentage. Note that the sum of all mass percents of a solution must total to 100%.

Sample Calculations Using Percent by Mass:

  1. What is the percent by mass of each component when 15.0 g of NaCl is and 20.0 g of KCl is placed in 125 g of water?


  2. How many grams of water must be added to 20.0 g of sucrose so that the solution has a percent by mass of sucrose equal to 6.50%?



  3. What is the molality and mole fraction of solute KI (molar mass = 166.0 g/mole) in solute water (molar mass = 18.0 g/mole) that has a percent by mass KCl of 18.2%?
    To make 18.2%, 100 grams of total solution contains 18.2 g of KI
    100 g - 18.2 g = 81.8 g water = 0.0818 kg



  4. A solution which is 5.65 percent by mass NaCl (molar mass = 58.44 g/mole) in water (molar mass = 18.0 g/mole) has a density of 1.06 g/mL. What is its molarity?
    To make 5.65%, 100 grams of total solution contains 5.65 g of NaCl



Practice Problems:
  1. What is the percent by mass of each component when 20.0 g of sucrose is mixed with 50.0 g of water? (Answer: Sucrose - 28.6%, Water - 71.4%)
  2. How many grams of sucrose must be added to 25.0 g of water to give a solution which has a percent by mass of sucrose equal to 12.0%? (Answer: 3.41 g)
  3. A solution of sucrose (molar mass = 342.3 g/mole) in water has density 1.10 g/mL and molarity 1.00 M. What is its percent by mass of sucrose? (Answer: 31.1%)
  4. A solution has percent by mass of 3.27% LiI (molar mass = 133.8 g/mole) in water (molar mass = 18.0 g/mole). What is its mole fraction? (Answer: XLiI = 0.00452)
  5. What is the percent by mass of solute KBr (molar mass = 119.0 g/mole) in a solution that has a molality of 0.450 m? (Answer: 5.08%)
  6. What is the percent by mass of solute KCl (molar mass = 74.6 g/mole) in solvent water (molar mass = 18.0 g/mole) if the solution has XKCl = 0.125? (Answer: 37.2%)
  7. How many grams of water must be mixed with 11.0 g of LiF to give a solution which has a percent by mass of LiF equal to 6.25%?(Answer: 165 g)
  8. What is the molality and mole fraction of a solution that has percent by mass of 1.15% LiF (molar mass = 25.9 g/mole) in water (molar mass = 18.0 g/mole)? (Answer: molality = 0.449 m, XLiF = 0.00802)

Find the Concentration of a Solution With Density

Source: https://www2.southeastern.edu/Academics/Faculty/wparkinson/help/concentration_units/