Question

gases are different from solids and liquids. in a sample of gas, the molecules are far apart. the gas molecules also move around slide with each other as well as with the walls of the container. these collisions generate pressure. the pressure of a gas can be measured in different units. one convenient unit of measure is called the atmosphere (atm) because it is based on atmospheric pressure. at sea level, the average pressure is 1 atm. as you get higher in altitude, the pressure steadily drops until you leave the atmosphere, where the pressure is very close to 0 atm.
the table below shows the different commonly used units of measuring gas pressure. use this table in the pressure unit conversions.

unit	abbreviation	1 atm equivalent
millimeters of mercury	mmhg	760 mmhg
torr	torr	760 torr
inches of mercury	in. hg	29.9 in. hg
pounds per square inch (psi)	lb/in.²	14.7 lb/in.²
pascal	pa	101325 pa

part c
high-pressure liquid chromatography (hplc) is a method used in chemistry and biochemistry to purify chemical substances. the pressures used in this procedure range from around 500 kilopascals (500,000 pa) to about 60,000 kpa (60,000,000 pa). it is often convenient to know the pressure in torr. if an hplc procedure is running at a pressure of 3.64×10⁸ pa, what is its running pressure in torr?
express the pressure numerically in torr.
view available hint(s)
3.64×10⁸ pa =

torr

Explanation:

Step1: Find conversion factor

From the table, \(1\ \text{atm} = 760\ \text{torr}\) and \(1\ \text{atm} = 101325\ \text{Pa}\). So, the conversion factor from Pa to torr is \(\frac{760\ \text{torr}}{101325\ \text{Pa}}\).

Step2: Apply conversion

Given pressure \(P = 3.64\times 10^{8}\ \text{Pa}\). Multiply by the conversion factor:
\(P_{\text{torr}} = 3.64\times 10^{8}\ \text{Pa} \times \frac{760\ \text{torr}}{101325\ \text{Pa}}\)
First, calculate \(3.64\times 10^{8} \times \frac{760}{101325}\):
\(\frac{3.64\times 10^{8} \times 760}{101325} \approx \frac{2.7664\times 10^{11}}{101325} \approx 2.73\times 10^{6}\) (after simplifying the arithmetic).

Answer:

\(2.73\times 10^{6}\) (or more precisely, after exact calculation: \(3.64\times10^{8} \times \frac{760}{101325} = \frac{3.64\times760\times10^{8}}{101325}=\frac{2766.4\times10^{8}}{101325}=\frac{276640000000}{101325}\approx 2730000\) or \(2.73\times 10^{6}\) torr)