Concept explainers
(a) Derive the equation relating the molality (m) of a solution to its molarity (M),
where d is the density of the solution (g/mL) and ℳ is the molar mass of the solute (g/mol). (Hint: Start by expressing the solvent in kilograms in terms of the difference between the mass of the solution and the mass of the solute.) (b) Show that, for dilute aqueous solutions, m is approximately equal to M.
(a)

Interpretation:
The given equation relating molality (m) of the solution to its molarity (M) has to be derived.
Concept introduction:
Molality (m): Molality is the number of moles of solute present in one kilogram of solvent.
Molarity (M): Molarity is number of moles of the solute present in the one liter of the solution.
Molarity is estimation of moles in the total volume of the solution while molality is estimation of moles in relationship with solvent in the solution
Explanation of Solution
Given data:
Where,
Relate molality (m) to molarity (M):
The equations relating the molality (m) of the solution to its molarity (M) are as follows,
If we assume 1L of the solution then we can determine the mass of the solution from its volume and density and the mass of the solute from molar mass and molarity.
Substituting these expressions into equation (1) we get,
From molality definition we know that,
We assume that 1L of the solution, we also know that mol solute (n) = Molarity (M), then the equation (3) becomes,
Substitute this expression into equation (2) we get,
Take inverse of both sides of the equations,
(b)

Interpretation:
For dilute aqueous solutions, m is approximately equal to M has to be shown.
Concept introduction:
Molality (m): Molality is the number of moles of solute present in one kilogram of solvent.
Molarity (M): Molarity is number of moles of the solute present in the one liter of the solution.
Molarity is estimation of moles in the total volume of the solution while molality is estimation of moles in relationship with solvent in the solution
Explanation of Solution
m is approximately equal to M For dilute aqueous solutions is shown as follows,
For dilute aqueous solution the density is approximately
In dilute solutions,
For example, 0.010M
The derived equation reduces to
Because
Want to see more full solutions like this?
Chapter 12 Solutions
CHEMISTRY 1111 LAB MANUAL >C<
- Complete the following equations hand written pleasearrow_forwardComplete the following equations please hand written pleasearrow_forwardUsing the Nernst equation to calculate nonstandard cell voltage A galvanic cell at a temperature of 25.0 °C is powered by the following redox reaction: 3+ 3Cu²+ (aq) +2Al(s) → 3 Cu(s)+2A1³* (aq) 2+ Suppose the cell is prepared with 5.29 M Cu in one half-cell and 2.49 M A1³+ in the other. Calculate the cell voltage under these conditions. Round your answer to 3 significant digits. x10 μ ☑ 00. 18 Ar Иarrow_forward
- Please help me solve this homework problemarrow_forwardPlease help me answer this homework questionarrow_forwardCalculating standard reaction free energy from standard reduction... Using standard reduction potentials from the ALEKS Data tab, calculate the standard reaction free energy AG° for the following redox reaction. Be sure your answer has the correct number of significant digits. 3+ H2(g)+2OH¯ (aq) + 2Fe³+ (aq) → 2H₂O (1)+2Fe²+ (aq) 0 kJ x10 Х ? olo 18 Ararrow_forward
- Calculating the pH of a weak base titrated with a strong acid An analytical chemist is titrating 184.2 mL of a 0.7800M solution of dimethylamine ((CH3) NH with a 0.3000M solution of HClO4. The pK₁ of dimethylamine is 3.27. Calculate the pH of the base solution after the chemist has added 424.1 mL of the HClO solution to it. 2 4 Note for advanced students: you may assume the final volume equals the initial volume of the solution plus the volume of HClO 4 solution added. Round your answer to 2 decimal places. pH = ☐ ☑ ? 000 18 Ar 1 Barrow_forwardUsing the Nernst equation to calculate nonstandard cell voltage A galvanic cell at a temperature of 25.0 °C is powered by the following redox reaction: MnO2 (s)+4H* (aq)+2Cr²+ (aq) → Mn²+ (aq)+2H₂O (1)+2Cr³+ (aq) + 2+ 2+ 3+ Suppose the cell is prepared with 7.44 M H* and 0.485 M Cr²+ in one half-cell and 7.92 M Mn² and 3.73 M Cr³+ in the other. Calculate the cell voltage under these conditions. Round your answer to 3 significant digits. ☐ x10 μ Х 5 ? 000 日。arrow_forwardCalculating standard reaction free energy from standard reduction... Using standard reduction potentials from the ALEKS Data tab, calculate the standard reaction free energy AG° for the following redox reaction. Be sure your answer has the correct number of significant digits. NO (g) +H₂O (1) + Cu²+ (aq) → HNO₂ (aq) +H* (aq)+Cu* (aq) kJ - ☐ x10 x10 olo 18 Ararrow_forward
- Calculating the pH of a weak base titrated with a strong acid b An analytical chemist is titrating 116.9 mL of a 0.7700M solution of aniline (C6H5NH2) with a 0.5300M solution of HNO3. The pK of aniline is 9.37. Calculate the pH of the base solution after the chemist has added 184.2 mL of the HNO 3 solution to it. Note for advanced students: you may assume the final volume equals the initial volume of the solution plus the volume of HNO3 solution added. Round your answer to 2 decimal places. pH = ☐ ☑ 5arrow_forwardQUESTION: Find the standard deviation for the 4 different groups 5.298 3.977 223.4 148.7 5.38 4.24 353.7 278.2 5.033 4.044 334.6 268.7 4.706 3.621 305.6 234.4 4.816 3.728 340.0 262.7 4.828 4.496 304.3 283.2 4.993 3.865 244.7 143.6 STDEV = STDEV = STDEV = STDEV =arrow_forwardQUESTION: Fill in the answers in the empty green boxes regarding 'Question 5: Calculating standard error of regression' *The images of the data showing 'coefficients for the standard curve' have been providedarrow_forward
- Chemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning
- Chemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage LearningIntroduction to General, Organic and BiochemistryChemistryISBN:9781285869759Author:Frederick A. Bettelheim, William H. Brown, Mary K. Campbell, Shawn O. Farrell, Omar TorresPublisher:Cengage LearningChemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage Learning





