Question

(a) Calculate the molarity of a solution that contains moles of protons are present in \(35.0 \mathrm{~mL}\) of a \(4.50 \mathrm{M}\) solution of nitric acid? (c) How many milliliters of a \(6.00 \mathrm{M} \mathrm{NaOH}\) solution are needed to provide \(0.350 \mathrm{~mol}\) of \(\mathrm{NaOH}\) ?

Short answer

(a) The molarity of protons in the solution is \(4.50 M\). (c) The volume of \(6.00 M\) NaOH solution needed to provide \(0.350 mol\) of NaOH is \(\frac{0.350}{6.00} \times 1000\, mL\).

Step-by-step solution

(a) Calculate moles of protons in nitric acid.

First, we need to calculate the moles of protons in 35.0 mL of a 4.50 M solution of nitric acid. Since the molarity(M) is defined as moles of solute per liter of solution, we can find the moles of the solute by multiplying the volume of the solution (in liters) by its molarity. Given, Volume= \(35.0 ml = 0.035 L\), and Molarity = \(4.50 M\). Moles of nitric acid = Molarity × Volume = \(4.50 M × 0.035 L\) #=tag_title#Calculate the moles of protons in the nitric acid solution.

Nitric acid (HNO₃) dissociates into a proton (H⁺) and nitrate (NO₃⁻) in aqueous solution. This means there are equal moles of protons in the solution as there are moles of nitric acid. Moles of protons = Moles of nitric acid = \(4.50 M × 0.035 L\) #=tag_title#Calculate molarity of protons.

Now that we have the moles of protons present in 35.0 mL of the solution, we can calculate the molarity of the protons within the solution as well. Molarity of protons = Moles of protons / Volume of solution (in liters) = \[(4.50 M × 0.035 L) / 0.035 L\] The volume of the solution (0.035 L) cancels out, making the molarity of protons equal to that of the nitric acid: Molarity of protons = \(4.50 M\)

(c) Convert moles of NaOH to volume.

In this part of the problem, we are given the molarity of the NaOH solution and the moles of NaOH needed. We should find the volume of this solution required to provide the given moles of NaOH. Given moles of NaOH = \(0.350 mol\), and Molarity of NaOH = \(6.00 M\). Molarity = Moles of solute / Volume of solution Volume of NaOH solution = Moles of solute / Molarity = \(0.350 mol / 6.00 M\)

Convert volume to milliliters.

To get the volume in milliliters, we need to convert the volume in liters to milliliters by multiplying by 1000. Volume of NaOH solution in mL = \((0.350 mol / 6.00 M) × 1000\, mL\) Now, we have the answers for both parts of the exercise: (a) The molarity of protons in the solution is 4.50 M. (c) The volume of 6.00 M NaOH solution needed to provide 0.350 mol of NaOH is \((0.350 mol / 6.00 M) × 1000\, mL\).

Key concepts

Protons Concentration

When dealing with acidic solutions like nitric acid ( HNO₃ ), the concentration of protons (H⁺ ions) is of key importance. Molarity, indicated by the symbol 'M', is a measure of the concentration of a solute in a solution — essentially, how many moles of solute exist in one liter of solution. Hence, in the case of acids like nitric acid, molarity tells us how concentrated the acid is in terms of protons supplied.

Nitric acid completely dissociates in an aqueous solution, meaning for each molecule of HNO₃ you have in the solution, it produces one H⁺ ion. Therefore, if you know the molarity of the nitric acid solution, you directly know the concentration of protons in that solution. A 4.50 M nitric acid solution, for instance, clearly shows that there are 4.50 moles of protons per liter of the solution. This direct relationship makes calculating proton concentration quite straightforward when dealing with strong, fully dissociating acids like HNO₃ .

Nitric Acid Dissociation

Nitric acid is a strong acid, which means it fully dissociates in water. The dissociation of nitric acid can be represented by the equation:
\[\mathrm{HNO_{3}(aq) \rightarrow H^{+}(aq) + NO_{3}^{-}(aq)}\]This equation shows that for every one molecule of nitric acid, one proton and one nitrate ion (NO₃⁻) are produced. The complete dissociation is crucial when considering how many protons are present, as each HNO₃ molecule yields one proton.

Understanding the dissociation helps in determining the molarity of protons in any aqueous solution of nitric acid. Since there is a one-to-one ratio of nitric acid to protons, if you dissolve a 4.50 M concentration of nitric acid in water, you can expect a 4.50 M concentration of protons. This is precisely why, when working out the concentration of protons, you can equate it directly to the molarity of the nitric acid itself.

NaOH Solution Volume

To find out how much of a sodium hydroxide (NaOH) solution is required to have a certain number of moles, you can use the molarity formula: Molarity is the number of moles of solute divided by the volume of the solution in liters.

For example, if you need 0.350 moles of NaOH and the solution available is 6.00 M, you can calculate the necessary volume using:

• Molarity (M) = Moles of solute / Volume of solution

Rearranging the formula gives us:\[\text{Volume of NaOH solution} = \frac{\text{Moles of solute}}{\text{Molarity}}\]\[= \frac{0.350 \text{ mol}}{6.00 \text{ M}}\]Once you compute this volume in liters, converting to milliliters involves simply multiplying by 1000, as there are 1000 mL in a liter. This conversion is straightforward and allows one to easily ascertain the exact volume needed. For application in a lab setting, this is extremely important when preparing precise solutions.