Question

the vapor pressure of water at (80\text{ }^{\circ}\text{c}) is (0.4675\text{ atm}). calculate the vapor pressure in (\text{kpa}).
be sure your answer has the right number of significant digits.

Explanation:

🆕 New Concept Discovered: Pressure Unit Conversion
Converting between different units of pressure using standard conversion factors.

Step 1: Identify the conversion factor

To convert from atmospheres (\(\text{atm}\)) to kilopascals (\(\text{kPa}\)), we use the standard relationship between these two units of pressure:

$$ 1\text{ atm} = 101.325\text{ kPa} $$

This means that for every \(1\text{ atm}\) of pressure, there are exactly \(101.325\text{ kPa}\).

Step 2: Set up the calculation

Multiply the given value in \(\text{atm}\) by the conversion factor to find the value in \(\text{kPa}\):

$$ 0.4675\text{ atm} \times \frac{101.325\text{ kPa}}{1\text{ atm}} $$

$$ 0.4675 \times 101.325 = 47.3694375\text{ kPa} $$

Step 3: Round to the correct number of significant digits

• The given value \(0.4675\text{ atm}\) has \(4\) significant digits (the leading zero is not significant).
• The conversion factor \(101.325\text{ kPa/atm}\) has \(6\) significant digits.
• When multiplying, the final answer must be rounded to the least number of significant digits present in the starting measurements, which is \(4\) significant digits.

Rounding \(47.3694375\) to \(4\) significant digits gives:

$$ 47.37\text{ kPa} $$

Answer:

47.37