Questions: Find partial pressure if PH is 7.5.

Find partial pressure if PH is 7.5.
Transcript text: Find partial pressure if PH is 7.5.
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Solution

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Solution Steps

Step 1: Understand the Given Equation

The given equation is:

\[ PH(x) = 6.1 + \log \left(\frac{800}{x}\right) \]

We need to find the value of \(x\) (partial pressure) when \(PH(x) = 7.5\).

Step 2: Set Up the Equation

Substitute \(PH(x) = 7.5\) into the equation:

\[ 7.5 = 6.1 + \log \left(\frac{800}{x}\right) \]

Step 3: Isolate the Logarithmic Term

Subtract 6.1 from both sides to isolate the logarithmic term:

\[ 7.5 - 6.1 = \log \left(\frac{800}{x}\right) \]

\[ 1.4 = \log \left(\frac{800}{x}\right) \]

Step 4: Solve for \(x\)

To solve for \(x\), rewrite the equation in exponential form:

\[ 10^{1.4} = \frac{800}{x} \]

Calculate \(10^{1.4}\):

\[ 10^{1.4} \approx 25.1189 \]

Now solve for \(x\):

\[ x = \frac{800}{25.1189} \]

\[ x \approx 31.8450 \]

Final Answer

The partial pressure \(x\) when \(PH(x) = 7.5\) is approximately:

\[ \boxed{x \approx 31.8450} \]

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