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3 votes
At a constant temperature, a sample of gas occupies 1.5 L at a pressure of 2.8 ATM. What will be the pressure of this sample, in atmospheres, if the new volume is 0.92 L?

User Tinny
by
8.1k points

2 Answers

3 votes

Answer:


\boxed {\boxed {\sf 4.6 \ atm}}

Step-by-step explanation:

We are asked to find the new pressure given a change in volume. We will use Boyle's Law, which states the volume of a gas is inversely proportional to the pressure. The formula for this law is:


P_1V_1= P_2V_2

Initially, the gas occupies 1.5 liters at a pressure of 2.8 atmospheres.


1.5 \ L * 2.8 \ atm = P_2V_2

The volume is changed to 0.92 liters, but the pressure is unknown.


1.5 \ L * 2.8 \ atm = P_2* 0.92 \ L

We are solving for the final pressure, so we must isolate the variable Pā‚‚. It is being multiplied by 0.92 liters. The inverse operation of multiplication is division, so we divide both sides by 0.92 L.


\frac {1.5 \ L * 2.8 \ atm}{0.92 \ L} = (P_2* 0.92 \ L)/(0.92 \ L)


\frac {1.5 \ L * 2.8 \ atm}{0.92 \ L}= P_2

The units of liters cancel each other out.


\frac {1.5 * 2.8 \ atm}{0.92 }=P_2


\frac {4.2}{0.92} \ atm= P_2


4.565217391 \ atm = P_2

The original measurements of pressure and volume have 2 significant figures, so our answer must have the same. For the number we calculated, that is the tenths place. The 6 in the hundredth place tells us to round the 5 up to a 6.


4.6 \ atm \approx P_2

The pressure is approximately 4.6 atmospheres.

User Jamie Hamick
by
8.4k points
5 votes
  • V1=1.5L
  • V2=0.92L
  • P1=2.8atm
  • P2=?

Using boyles law


\boxed{\sf v\propto (1)/(p)}


\\ \sf\longmapsto P_1V_1=P_2V_2


\\ \sf\longmapsto P_2=(P_1V_1)/(V_2)


\\ \sf\longmapsto P_2=(2.8* 1.5)/(0.92)


\\ \sf\longmapsto P_2=(4.2)/(0.92)


\\ \sf\longmapsto P_2=4.56atm


\\ \sf\longmapsto P_2\approx 4.6atm

User Mrconcerned
by
8.1k points
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