The acidity of a solution is measured by its pH . If $$ \left[\mathrm{H}^{+}\right] $$represents the concentration of hydrogen ions (in moles/liter) in the solution, the pH is defined by Suppose a solution has $$ \mathrm{pH}=2.28 $$. $$ \mathrm{pH}=-\log \left[\mathrm{H}^{+}\right] $$ (a) Rewrite the logarithmic form of the equation into exponential form. ( $$ \Leftrightarrow $$ indicates two way equivalence) - $$ \log \left[\mathrm{H}^{+}\right]=\mathrm{pH} \Leftrightarrow $$ Click for List $$ \left[\mathrm{H}^{+}\right] \approx 0.00263 $$ moles/liter $$ \left[\mathrm{H}^{+}\right] \approx 2.7938 $$ moles/liter $$ \left[\mathrm{H}^{+}\right] \approx 0.00525 $$ moles/liter $$ \left[\mathrm{H}^{+}\right] \approx-190.5461 $$ moles/liter $$ \left[\mathrm{H}^{+}\right] \approx 0.4386 $$ moles/liter $$ \left[\mathrm{H}^{+}\right] \approx-0.3579 $$ moles/liter $$ \left[\mathrm{H}^{+}\right] \approx 0.3579 $$ moles/liter

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UpStudy AI · Accepted Answer

To solve the problem, we need to follow these steps:

1. **Rewrite the logarithmic form into exponential form**:
   The equation given is:
   $$
   \text{pH} = -\log \left[\mathrm{H}^{+}\right]
   $$
   This can be rewritten in exponential form as:
   $$
   \left[\mathrm{H}^{+}\right] = 10^{-\text{pH}}
   $$

2. **Substitute the given pH value**:
   We are given that $$\text{pH} = 2.28$$. We can substitute this value into the exponential form:
   $$
   \left[\mathrm{H}^{+}\right] = 10^{-2.28}
   $$

3. **Calculate the concentration of hydrogen ions**:
   Now, we will calculate $$10^{-2.28}$$ to find the concentration $$\left[\mathrm{H}^{+}\right]$$.

Let's perform the calculation.
Calculate the value by following steps:
- step0: Calculate:
  $$10^{-2.28}$$
- step1: Convert the expressions:
  $$10^{-\frac{57}{25}}$$
- step2: Express with a positive exponent:
  $$\frac{1}{10^{\frac{57}{25}}}$$
- step3: Simplify:
  $$\frac{1}{100\sqrt[25]{10^{7}}}$$
- step4: Multiply by the Conjugate:
  $$\frac{\sqrt[25]{10^{18}}}{100\sqrt[25]{10^{7}}\times \sqrt[25]{10^{18}}}$$
- step5: Multiply the numbers:
  $$\frac{\sqrt[25]{10^{18}}}{1000}$$
The calculation gives us:

$$
\left[\mathrm{H}^{+}\right] \approx 0.005248 \text{ moles/liter}
$$

Now, let's summarize the results:

- The exponential form of the equation is:
  $$
  \left[\mathrm{H}^{+}\right] = 10^{-\text{pH}} \Leftrightarrow \left[\mathrm{H}^{+}\right] \approx 0.00525 \text{ moles/liter}
  $$

Thus, the correct answer from the options provided is:
$$
\left[\mathrm{H}^{+}\right] \approx 0.00525 \text{ moles/liter}
$$
$$ \left[\mathrm{H}^{+}\right] \approx 0.00525 \text{ moles/liter} $$

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