Answer:
4.45 atm
Explanation:
Applying,
PV = P'V'............ Equation 1
Where P = Initial pressure of the container, V = Initial volume of the container, P' = Final pressure of the container, V' = Final volume of the container.
make P the subject of the equation
P = P'V'/V........... Equation 2
From the question,
Given: V = 55.2 L, P' = 8.53 atm, V' = 28.8 L
Substitute these values into equation 2
P = (8.53×28.8)/55.2
P = 4.45 atm
Answer:
[tex]\boxed {\boxed {\sf 4.45 \ atmospheres}}[/tex]
Explanation:
We are asked to find the pressure given a change in volume. The temperature remains constant, so we are only concerned with volume and pressure. 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:
[tex]P_1 V_1= P_2V_2[/tex]
The initial pressure is unknown, but the volume starts at 55.2 liters.
[tex]P_1 * 55.2 \ L = P_2V_2[/tex]
The volume is reduced to 28.8 liters and the pressure is 8.53 atmospheres.
[tex]P_1 * 55.2 \ L = 8.53 \ atm * 28.8 \ L[/tex]
We are solving for the initial pressure, so we must isolate the variable P₁. It is being multiplied by 55.2 liters. The inverse operation of multiplication is division, so we divide both sides of the equation by 55.2 L.
[tex]\frac {P_1 * 55.2 \ L }{55.2 \ L}= \frac{8.53 \ atm * 28.8 \ L}{55.2 \ L}[/tex]
[tex]P_1= \frac{8.53 \ atm * 28.8 \ L}{55.2 \ L}[/tex]
The units of liters (L) cancel.
[tex]P_1= \frac{8.53 \ atm * 28.8 }{55.2}[/tex]
[tex]P_1=\frac{245.664 }{55.2 } \ atm[/tex]
[tex]P_1 = 4.45043478261 \ atm[/tex]
The original measurements of volume and pressure have 3 significant figures, so our answer must have the same. For the number we calculated, that is the hundredths place. The 0 in the thousandths place tells us to leave the 5.
[tex]P_1 \approx 4.45 \ atm[/tex]
The initial pressure inside the container is approximately 4.45 atmospheres.
