Question

convert 281.1 kpa to torr. report your answer to the nearest whole number.

Explanation:

Step1: Recall the conversion factor

We know that \(1\space \text{kPa} = 7.50062\space \text{Torr}\) (approximately, more accurately \(1\space \text{atm}=101.325\space \text{kPa}=760\space \text{Torr}\), so \(1\space \text{kPa}=\frac{760}{101.325}\approx7.50062\space \text{Torr}\))

Step2: Multiply the given value by the conversion factor

We have \(281.1\space \text{kPa}\). To convert to Torr, we multiply by the conversion factor:
\(281.1\times7.50062\)

First, calculate \(281\times7.50062 = 281\times7+281\times0.50062=1967 + 140.67422 = 2107.67422\)
Then, \(0.1\times7.50062 = 0.750062\)
Adding them together: \(2107.67422+0.750062 = 2108.424282\)

Using the more accurate conversion from \(1\space \text{atm}=101.325\space \text{kPa}=760\space \text{Torr}\), so \(1\space \text{kPa}=\frac{760}{101.325}\space \text{Torr}\)

So \(281.1\times\frac{760}{101.325}=\frac{281.1\times760}{101.325}\)

Calculate numerator: \(281.1\times760 = 281.1\times700+281.1\times60=196770 + 16866=213636\)

Then divide by \(101.325\): \(\frac{213636}{101.325}\approx2108\) (when rounded to the nearest whole number)

Answer:

\(2108\) (if we use the more accurate \(\frac{760}{101.325}\) conversion factor: \(\frac{281.1\times760}{101.325}=\frac{213636}{101.325}=2108.424\approx2108\) when rounded to the nearest whole number)