How many times is the `H^+` concentration in the blood (pH =7.36) greater than in the spinal fluid (pH =7:53)?

Answer

To determine how many times the \( H^+ \) concentration in the blood is greater than in the spinal fluid, we can follow these steps:

### Step 1: Understand the relationship between pH and \( H^+ \) concentration
The \( H^+ \) concentration can be calculated from the pH using the formula:
\[ [H^+] = 10^{-\text{pH}} \]

### Step 2: Calculate the \( H^+ \) concentration in the blood
Given that the pH of the blood is 7.36, we can calculate the \( H^+ \) concentration in the blood:
\[ [H^+]_{\text{blood}} = 10^{-7.36} \]

### Step 3: Calculate the \( H^+ \) concentration in the spinal fluid
Given that the pH of the spinal fluid is 7.53, we can calculate the \( H^+ \) concentration in the spinal fluid:
\[ [H^+]_{\text{spinal fluid}} = 10^{-7.53} \]

### Step 4: Set up the ratio of \( H^+ \) concentrations
To find out how many times the \( H^+ \) concentration in the blood is greater than that in the spinal fluid, we take the ratio:
\[ \text{Ratio} = \frac{[H^+]_{\text{blood}}}{[H^+]_{\text{spinal fluid}}} = \frac{10^{-7.36}}{10^{-7.53}} \]

### Step 5: Simplify the ratio using properties of exponents
Using the property of exponents, we can simplify the ratio:
\[ \text{Ratio} = 10^{-7.36 + 7.53} = 10^{0.17} \]

### Step 6: Calculate the numerical value of the ratio
Now we can calculate \( 10^{0.17} \):
\[ 10^{0.17} \approx 1.5 \]

### Conclusion
Thus, the \( H^+ \) concentration in the blood is approximately 1.5 times greater than that in the spinal fluid.