How many liters of distilled water must be added to 1 liter of an aqueous solution of HCl with a pH of 1 to create a solution with a pH of 2? (A) 0.1 L (B) 0.9 L (C) 2 L (D) 9 L

Short Answer

Expert verified
The answer is (D) 9 L.

Step by step solution

01

Determine initial concentration of \(H_3O^+\) ions

From the definition of pH, we can determine the initial concentration, \(C_1\), of \(H_3O^+\) ions in the HCl solution by using the equation \(C_1=10^{-pH}\). So, when \(pH=1\), \(C_1=10^{-1}=0.1\) M (moles per liter).
02

Determine final concentration of \(H_3O^+\) ions

We will also aim for a final concentration, \(C_2\), of \(H_3O^+\) ions that would give a pH of 2. Similarly, we use the equation \(C_2=10^{-pH}\). So, when pH=2, \(C_2=10^{-2}=0.01\) M.
03

Calculate the volume of distilled water to be added

In order to reach the intended concentration, the same amount of substance (moles of \(H_3O^+\)) needs to be diluted with a total of 10 volumes (because \(C_1/C_2 = 10\)), which means adding 9 volumes of water to the initial one. Therefore, 9 liters of distilled water should be added to the solution.

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Most popular questions from this chapter

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A solution of \(\mathrm{Co}^{2+}\) ions appears red when viewed under white light. Which of the following statements is true about the solution? (A) A spectrophotometer set to the wavelength of red light would read a high absorbance. (B) If the solution is diluted, the amount of light reflected by the solution will decrease. (C) All light with a frequency that is lower than that of red light will be absorbed by it. (D) Electronic transmissions within the solution match the wavelength of red light.

\(\begin{array}{ll}{\mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)} & {\Delta H^{\circ}=-390 \mathrm{kJ} / \mathrm{mol}} \\\ {\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)} & {\Delta H^{\circ}=-290 \mathrm{kJ} / \mathrm{mol}} \\ {2 \mathrm{C}(s)+\mathrm{H}_{2}(g) \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(g)} & {\Delta H^{\circ}=+230 \mathrm{kJ} / \mathrm{mol}}\end{array}\) Based on the information given above, what is \(\Delta H^{\circ}\) for the following reaction? $$ \begin{aligned} \mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \\ \text { (A) }-1,300 \mathrm{kJ} \\ \text { (B) }-1,070 \mathrm{kJ} \\ \text { (C) }-840 \mathrm{kJ} \\ \text { (D) }-780 \mathrm{kJ} \end{aligned} $$

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