To solve the problem of finding the hydrogen ion concentration [tex]\([\text{H}^+]\)[/tex] for given pH values for two substances, we will follow the definition of pH. The pH of a solution is defined by the formula:
[tex]\[ \text{pH} = -\log[\text{H}^+] \][/tex]
We can rearrange this formula to solve for the hydrogen ion concentration:
[tex]\[ [\text{H}^+] = 10^{-\text{pH}} \][/tex]
Now we will apply this formula to both the given pH values.
### (a) Tomatses: [tex]\( \text{pH} = 4.1 \)[/tex]
1. Calculate the hydrogen ion concentration [tex]\([\text{H}^+]\)[/tex]:
[tex]\[ [\text{H}^+] = 10^{-4.1} \][/tex]
2. Expressing the result in scientific notation and rounding to one decimal place:
[tex]\[ 10^{-4.1} = 7.943282347242822 \times 10^{-5} \][/tex]
Rounded to one decimal place and in scientific notation, this becomes:
[tex]\[ [\text{H}^+] \approx 7.9 \times 10^{-5} \, \text{M} \][/tex]
Thus, for Tomatses,
[tex]\[ \left[ \text{H}^+ \right] = 7.9 \times 10^{-5} \, \text{M} \][/tex]
### (b) Human blood: [tex]\( \text{pH} = 7.3 \)[/tex]
1. Calculate the hydrogen ion concentration [tex]\([\text{H}^+]\)[/tex]:
[tex]\[ [\text{H}^+] = 10^{-7.3} \][/tex]
2. Expressing the result in scientific notation and rounding to one decimal place:
[tex]\[ 10^{-7.3} = 5.011872336272725 \times 10^{-8} \][/tex]
Rounded to one decimal place and in scientific notation, this becomes:
[tex]\[ [\text{H}^+] \approx 5.0 \times 10^{-8} \, \text{M} \][/tex]
Thus, for human blood,
[tex]\[ \left[ \text{H}^+ \right] = 5.0 \times 10^{-8} \, \text{M} \][/tex]
### Summary:
(a) Tomatses:
[tex]\[ \left[ \text{H}^+ \right] \approx 7.9 \times 10^{-5} \, \text{M} \][/tex]
(b) Human blood:
[tex]\[ \left[ \text{H}^+ \right] \approx 5.0 \times 10^{-8} \, \text{M} \][/tex]
