Analyze and solve the following problem.
1.At 0 degrees celsius and 5 atm a given example of gas occupies 75L.The gas compressed to a final volume of 30L.What is the final pressure?
2.under constant pressure condition,a sample of hydrogen gas initially at 85 degrees celsius and 7.2L is cooled until its final volume is 4.1L .What is the final temperature?
3.a balloon containing 2 moles of helium has a volume of 0.8L what would the volume if 3.5 moles of helium are added to the balloon?
1.At 0 degrees celsius and 5 atm a given example of gas occupies 75L.The gas compressed to a final volume of 30L.What is the final pressure?
2.under constant pressure condition,a sample of hydrogen gas initially at 85 degrees celsius and 7.2L is cooled until its final volume is 4.1L .What is the final temperature?
3.a balloon containing 2 moles of helium has a volume of 0.8L what would the volume if 3.5 moles of helium are added to the balloon?
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1) Boyles Law
P1V1 = P2V2
where in, P1 = first pressure
V1 = first volume
P2 = second pressure
V2 = second volume
Note: Boyles Law because the given
above states the the temperature was
at 0°C, meaning, at constant state.
Given: P1 = 5atm
V1 = 75L
V2 = 30L
Unknown: P2 = ?
Formula: P2 = P1V1 / V2
Note: To get the formula, apply
division and cancellation of like terms
using the original formula of Boyles
Law.
P1V1 = P2V2 ← divide both sides by V2
P1V1 / V2 = P2V2 / V2 ← cancel like
terms
P1V1 / V2 = P2 ← final formula for P2
Solution: P2 = P1V1 / V2
= (5atm)(75L) / 30L
= 375atm•L / 30L
= 12.5atm
Note: "L" is cancelled out, so the unit
for pressure will remain which is "atm".
Final Answer: P2 = 12.5atm
2) Charles Law
V1/T1 = V2/T2
where in, V1 = first volume
T1 = first temperature
V2 = second volume
T2 = second temperature
Given: V1 = 7.2L
T1 = 358.15K
V2 = 4.1L
Note: Dealing with Temperature from
each of the Gas Law must always be
in Kelvin.
°C → K
85°C + 273.15K = 358.15K
Unknown: T2 = ?
Formula: T2 = V2T1 / V1
Note: To get the formula, apply
cross-multiplication, division and
cancellation of like terms using the
original formula of Charles Law.
V1/T1 = V2/T2 ← cross-multiply
V1T2 = V2T1 ← divide both sides by V1
V1T2 / V1 = V2T1 / V1 ← cancel like
terms
T2 = V2T1 / V1 ← final formula for T2
Solution: T2 = V2T1 / V1
= (4.1L)(358.15K) / 7.2L
= 1468.415L•K / 7.2L
= 203.95K
Note: "L" is cancelled out, so the unit
for temperature will remain which is
"K".
Final Answer: T2 = 203.95K
3) Avogadro's Law
V1/n1 = V2/n2
where in, V1 = first volume
n1 = first mole
V2 = second volume
n2 = second mole
Given: V1 = 0.8L
n1 = 2mol
n2 = 3.5mol
Unknown: V2 = ?
Formula: V2 = V1n2 / n1
Note: To get the formula, apply
cross-multiplication, division and
cancellation of like terms using the
original formula of Avogadro's Law.
V1/n1 = V2/n2 ← cross-multiply
V1n2 = V2n1 ← divide both sides by n1
V1n2 / n1 = V2n1 / n1 ← cancel like
terms
V1n2 / n1 = V2 ← final formula for V2
Solution: V2 = V1n2 / n1
= (0.8L)(3.5mol) / 2mol
= 2.8L•mol / 2mol
= 1.4L
Note: "mol" is cancelled out, so the
unit for volume will remain which is "L".
Final Answer: V2 = 1.4L
Reminder: Cancellation of units is
applicable when the other same unit is
on the denominator.
Tip: To determine easily what Gas Law
must use in a certain problem, look
first for the given.