Q. 8.15 - An Introduction to General, Organic, and Biological Chemistry

Question

A I0.0-L balloon contains helium gas at a pressure of 655 mmHg. What is the final pressure, in millimeters of mercury, when the helium is placed in tanks that have the following volumes, if there is no change in temperature and amount of gas? 

a. 20.0 L 

b. 2.50 L

c. 13 800 mL 

d. 1250 mL

Step-by-Step Solution

Answer

a. The final pressure, in millimeters of mercury, when the helium is placed in tanks that has the volume of$20.0 L$ is $327.5$mmHg.

b. The final pressure, in millimeters of mercury, when the helium is placed in tanks that has the volume of $2.50 L$ is $2620$mmHg.

c. The final pressure, in millimeters of mercury, when the helium is placed in tanks that has the volume of $13800$ml is $474.6$mmHg.

d. The final pressure, in millimeters of mercury, when the helium is placed in tanks that has the volume of $1250$ml is $5240$mmHg.

Part(a) Step 1: Given information

We need to find the final pressure when helium is placed in tank of volume $20.0 L$.

Part(a) Step 2: Explanation

We can use the Boyle's law to find the new pressure. 

$P1V1=P2V2$

Now $P1=655$mmHg

$V1=10.0 L$

$V2=20.0 L$

$P2=P1V1/V2$

Substituting the values we get,

$P2=\frac{ 655 mmHg \times 10 L}{20 L}=327.5$mmHg

Part(b) Step 1: Given information

We need to find the final pressure when helium is placed in tank of volume $2.50 L$

Part(b) Step 2: Explanation

We can use the Boyle's law to find the new pressure. 

$P1V1=P2V2$

Now $P1=655$mmHg

$V1=10.0 L$

$V2=2.50 L$

Substituting the values we get,

$P2=\frac{ 655 mmHg\times 10 L}{2.50 L}= 2620$mmHg

Part(c) Step 1: Given information

We need to find the final pressure when helium is placed in tank of volume $13800 ml$

Part(c) Step 2: Explanation

We can use the Boyle's law to find the new pressure. 

Now $P1=655$mmHg

$V1=10.0 L$

$V2=13800 ml$

$P2=P1V1/V2$

Substituting the values we get,

$P2=\frac{655 mmHg\times 10 L}{13800 ml}=474.6$mmHg

Part(d) Step 1: Given information

We need to find the final pressure when helium is placed in tank of volume $1250 ml$.

Part(d) Step 2: Explanation

We can use the Boyle's law to find the new pressure. 

Now $P1=655$mmHg

$V1=10.0 L$

$V2=1250 ml$

$P2=P1V1/V2$

Substituting the values we get,

$P2=5240$mmHg