Question

If we took 1.68 L of gas at 99.6 kPa and compressed to a pressure of 6,000,000 kPa, what would the volume of that gas be in microliters?

Microliter is one millionth of a liter.
Synthetic diamonds can be manufactured at pressures of 6,000,000 kPa

Answer 1

`color(red)(V_2="27.9 µL")`

Explanation:

Boyle's Law states that `P`and `V` are inversely proportional.

`P_1V_1=P_2V_2`

First, convert litres to microlitres.

`1.68cancelL xx ("1,000,000 μL")/(1cancelL)="1,680,000 μL"=1.68 xx10^6color(white)(l)"μL"`

`P_1=color(red)"99.6 kPa"`
`V_1="1.68 L" = color(red)(1.68 xx10^6color(white)(l)"μL")`
`P_2=color(red)(6.00 xx 10^6color(white)(l)kPa)`
`V_2=color(red)(?)`

Now, calculate the new volume.

`V_2=(P_1V_1)/(P_2)`
`V_2=color(red)((99.6cancel(kPa)(1.68 xx10^6color(white)(l)"μL"))/color(red)(6.00 xx10^6cancel(kPa)`
`V_2=color(red)("27.9 µL")`