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[H^(+)]=10^(-pH)

pH is a measure of the hydrogen ion concentration, 
[H^(+)], measured in moles per liter, of a solution. Solutions with a high concentration of hydrogen ions have a low 
pH and solutions with a low concentration of hydrogen ions have a high 
pH. The relationship between 
[H^(+)]and 
pH is shown in the equation. What is the effect on 
pH if the hydrogen ion concentration is multiplied by 10 ?
Choose 1 answer:
(A) The 
pH increases by 1 .
(B) The 
pH is multiplied by 10 .
(C) The 
pH is divided by 10 .
(D) The 
pH decreases by 1.

[H+]=10pH \left[H^{+}\right]=10^{-\mathrm{pH}} \newlinepH \mathrm{pH} is a measure of the hydrogen ion concentration, [H+] \left[\mathrm{H}^{+}\right] , measured in moles per liter, of a solution. Solutions with a high concentration of hydrogen ions have a low pH \mathrm{pH} and solutions with a low concentration of hydrogen ions have a high pH \mathrm{pH} . The relationship between [H+] \left[\mathrm{H}^{+}\right] and pH \mathrm{pH} is shown in the equation. What is the effect on pH \mathrm{pH} if the hydrogen ion concentration is multiplied by 1010 ?\newlineChoose 11 answer:\newline(A) The pH \mathrm{pH} increases by 11 .\newline(B) The pH \mathrm{pH} is multiplied by 1010.\newline(C) The pH \mathrm{pH} is divided by 1010 .\newline(D) The pH \mathrm{pH} decreases by 11 .

Full solution

Q. [H+]=10pH \left[H^{+}\right]=10^{-\mathrm{pH}} \newlinepH \mathrm{pH} is a measure of the hydrogen ion concentration, [H+] \left[\mathrm{H}^{+}\right] , measured in moles per liter, of a solution. Solutions with a high concentration of hydrogen ions have a low pH \mathrm{pH} and solutions with a low concentration of hydrogen ions have a high pH \mathrm{pH} . The relationship between [H+] \left[\mathrm{H}^{+}\right] and pH \mathrm{pH} is shown in the equation. What is the effect on pH \mathrm{pH} if the hydrogen ion concentration is multiplied by 1010 ?\newlineChoose 11 answer:\newline(A) The pH \mathrm{pH} increases by 11 .\newline(B) The pH \mathrm{pH} is multiplied by 1010.\newline(C) The pH \mathrm{pH} is divided by 1010 .\newline(D) The pH \mathrm{pH} decreases by 11 .
  1. Understanding pH and [H(+)]: Understand the relationship between [H(+)] and pH.\newlineThe equation [H(+)]=10pH[H^{(+)}] = 10^{-\text{pH}} shows that the pH is the negative logarithm (base 1010) of the hydrogen ion concentration. This means that if the hydrogen ion concentration increases, the pH value decreases, and vice versa.
  2. Effect of Multiplying [H+]:</b>Determinetheeffectofmultiplying$[H+][\text{H}^+]:</b> Determine the effect of multiplying \$[\text{H}^+] by 1010.\newlineIf the hydrogen ion concentration [H+][\text{H}^+] is multiplied by 1010, the new concentration becomes 10×[H+]10 \times [\text{H}^+]. We need to find out how this affects the pH.
  3. Applying the Change to the Equation: Apply the change to the equation.\newlineThe new hydrogen ion concentration is 10×[H+]10 \times [\mathrm{H}^{+}], so we substitute this into the equation:\newline[H+]=10×[H+]=10×10pH=101×10pH=101pH[\mathrm{H}^{+}]' = 10 \times [\mathrm{H}^{+}] = 10 \times 10^{-\text{pH}} = 10^{1} \times 10^{-\text{pH}} = 10^{1-\text{pH}}
  4. Finding the New pH Value: Find the new pH value.\newlineTo find the new pH, we take the negative logarithm (base 1010) of the new hydrogen ion concentration:\newlinepH' = log([H+])=log(101pH)=1pH-\log([H^{+}]') = -\log(10^{1-\text{pH}}) = 1 - \text{pH}
  5. Calculating the Change in pH: Calculate the change in pH.\newlineThe change in pH is the difference between the new pH and the original pH:\newlineΔpH=pHpH=(1pH)pH=12pH\Delta\text{pH} = \text{pH}' - \text{pH} = (1 - \text{pH}) - \text{pH} = 1 - 2\text{pH}\newlineSince we are only multiplying [H(+)][\text{H}^{(+)}] by 1010 once, the change in pH is simply 11 unit. Therefore, the pH decreases by 11.

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