At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine the hydronium ion concentration [tex]\(\left[ \text{H}_3\text{O}^+ \right]\)[/tex] given the pH of a solution, we use the definition of pH, which is:
[tex]\[ \text{pH} = -\log \left( \left[ \text{H}_3\text{O}^+ \right] \right) \][/tex]
Given this equation, we can solve for [tex]\(\left[ \text{H}_3\text{O}^+ \right]\)[/tex] by rearranging it as follows:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 10^{-\text{pH}} \][/tex]
In this specific problem, the pH is given as 3.40. Plugging in the value of pH into the formula, we get:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 10^{-3.40} \][/tex]
Evaluating this expression yields:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 0.00039810717055349735\; \text{M} \][/tex]
To express this in scientific notation for easier comparison with the given options, we can rewrite it as:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 3.98 \times 10^{-4}\; \text{M} \][/tex]
Thus, the correct answer is:
[tex]\[ 3.98 \times 10^{-4}\; \text{M} \][/tex]
Therefore, the [tex]\(\left[ \text{H}_3\text{O}^+ \right]\)[/tex] for the solution is:
[tex]\[ \boxed{3.98 \times 10^{-4}\; \text{M}} \][/tex]
[tex]\[ \text{pH} = -\log \left( \left[ \text{H}_3\text{O}^+ \right] \right) \][/tex]
Given this equation, we can solve for [tex]\(\left[ \text{H}_3\text{O}^+ \right]\)[/tex] by rearranging it as follows:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 10^{-\text{pH}} \][/tex]
In this specific problem, the pH is given as 3.40. Plugging in the value of pH into the formula, we get:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 10^{-3.40} \][/tex]
Evaluating this expression yields:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 0.00039810717055349735\; \text{M} \][/tex]
To express this in scientific notation for easier comparison with the given options, we can rewrite it as:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 3.98 \times 10^{-4}\; \text{M} \][/tex]
Thus, the correct answer is:
[tex]\[ 3.98 \times 10^{-4}\; \text{M} \][/tex]
Therefore, the [tex]\(\left[ \text{H}_3\text{O}^+ \right]\)[/tex] for the solution is:
[tex]\[ \boxed{3.98 \times 10^{-4}\; \text{M}} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.