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Chapter 14: Problem 76

To what volume must a solution of \(80.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{SO}_{4}\) in \(500.0 \mathrm{~mL}\) of solution be diluted to give a \(0.10 \mathrm{M}\) solution?

Short Answer

Expert verified
To dilute to a 0.10 M solution, the volume must be adjusted to 4.00 L.

Step by step solution

01

Calculate moles of H2SO4

Use the molar mass of H2SO4 to convert grams to moles. The molar mass of H2SO4 is approximately 98.09 g/mol. So, the number of moles of H2SO4 is calculated as: moles = mass (g) / molar mass (g/mol) = 80.0 g / 98.09 g/mol.
02

Calculate Initial Molarity

Using the initial volume of the solution, calculate the initial molarity (M1). M1 = moles of solute / volume of solution (L). Remember to convert the volume from milliliters to liters by dividing by 1000.
03

Apply Dilution Formula

Use the formula M1V1 = M2V2 to find the final volume (V2) after dilution, where M1 is the initial molarity, V1 is the initial volume, M2 is the final molarity and V2 is the final volume to find. We rearrange the formula to solve for V2: V2 = (M1V1) / M2.
04

Calculate Final Volume

Now, substitute the known values into the equation to calculate V2. Use the initial molarity from Step 2, initial volume of 0.500 L and the desired final molarity of 0.10 M.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity Calculation
Molarity, often represented by the symbol 'M', is a measurement of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. In simpler terms, it tells us how much of a substance is dissolved in a given volume of liquid.

To calculate molarity, you can use the formula:
\[ M = \frac{moles~of~solute}{volume~of~solution~in~liters} \]
For a student working to understand molarity, it's crucial to remember that molarity is a ratio. It represents the solute-to-solvent relationship in a very specific way, and being comfortable with this concept is key to mastering chemistry solutions.
Converting Grams to Moles
The bridge between the mass of a substance and the number of particles, like atoms or molecules, is its molar mass. This value is specific to each substance and is measured in grams per mole (g/mol).

To convert the mass of a substance to the number of moles, you can use the following formula:
\[ moles = \frac{mass~(g)}{molar~mass~(g/mol)} \]
Understanding this conversion is essential because chemical reactions and solution chemistry are generally discussed in terms of moles rather than grams. This ensures that the calculations are based on the number of particles involved, which dictates how substances interact chemically.
Molar Mass of H2SO4
The molar mass of a compound is the sum of the masses of all the atoms in one mole of the compound. For sulfuric acid (H2SO4), this involves adding twice the atomic mass of hydrogen (H), the atomic mass of sulfur (S), and four times the atomic mass of oxygen (O).

The atomic masses are approximately:
  • Hydrogen (H): 1.01 g/mol
  • Sulfur (S): 32.07 g/mol
  • Oxygen (O): 16.00 g/mol
By summing these up, we get:
\[ 2(1.01~g/mol) + 32.07~g/mol + 4(16.00~g/mol) = 98.09~g/mol \]
It's critical for students to learn how to compute the molar mass correctly as it is a fundamental step in various calculations in chemistry, including molarity.
Dilution Formula
Dilution involves making a solution less concentrated by adding more solvent. The dilution formula is a mathematical way to express the relationship between the concentrations and volumes before and after the dilution process.

The formula is given as:
\[ M1V1 = M2V2 \]
where M1 and V1 are the initial molarity and volume, and M2 and V2 are the final molarity and volume after dilution. To attain a specific concentration, this formula helps determine how much more solvent should be added. For students, practicing with this formula reinforces the concept of conservation of mass - the number of moles of solute remains the same, only the volume changes.

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Most popular questions from this chapter

Dark streaks have been observed on the surface of Mars These streaks sometimes seem to run or flow, and other times they appear static. It has been hypothesized that these streaks are salt (sodium chloride) water rivers that are sometimes melted, allowing them to flow, and at other times these rivers are frozen. If the salt water mixtures melt when the temperature rises to \(-12.7^{\circ} \mathrm{C}\), what is the molality of salt in the rivers? (Hint: The freezing point is determined by the molality of ions. How will the molality of sodium chloride be related to the molality of the ions?)

\- Use the equation to calculate the following: $$ \mathrm{K}_{2} \mathrm{CO}_{3}(a q)+2 \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q) \longrightarrow $$ \(2 \mathrm{KC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)\) (a) the moles of \(\mathrm{H}_{2} \mathrm{O}\) that can be obtained from \(25.0 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) (b) the volume of \(0.210 \quad M \mathrm{~K}_{2} \mathrm{CO}_{3}\) needed to produce \(17.5 \mathrm{~mol} \mathrm{KC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) (c) the volume of \(1.25 \mathrm{M} \mathrm{HC} \mathrm{H}_{2} \mathrm{H}_{2}\) needed to react with \(75.2 \mathrm{~mL} 0.750 \mathrm{M} \mathrm{K}_{2} \mathrm{CO}_{3}\) (d) the molarity \((M)\) of the \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution when \(10.15 \mathrm{~mL}\) react with \(18.50 \mathrm{~mL}\) of \(0.250 \mathrm{MK}_{2} \mathrm{CO}_{3}\) (e) the liters of \(\mathrm{CO}_{2}\) gas at STP produced by the reaction of \(105 \mathrm{~mL}\) of \(1.5 \mathrm{M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) (f) the liters of \(\mathrm{CO}_{2}\) gas at STP produced by the reaction of \(25.0 \mathrm{~mL}\) of \(0.350 M \mathrm{~K}_{2} \mathrm{CO}_{3}\) and \(25.0 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)

What happens to sugar molecules \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) when they are dissolved in water?

As you are studying for finals, you calculate the concentration of caffeine in an energy drink and discover that it is \(0.02080 \mathrm{M}\) in caffeine. If a cup of your favorite coffee contains \(254 \mathrm{mg}\) of caffeine, how many \(\mathrm{mL}\) of the energy drink will provide the same amount of caffeine? The molecular formula of caffeine is \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\).

Which would be more effective as an antifreeze in an automobile radiator? A solution containing (a) \(10 \mathrm{~kg}\) of methyl alcohol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) or \(10 \mathrm{~kg}\) of ethyl alcohol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right) ?\) (b) \(10 \mathrm{~m}\) solution of methyl alcohol or \(10 \mathrm{~m}\) solution of ethyl alcohol?
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