Question

how much work is done when a gas expands from an initial volume of 112 ml to a final volume of 155 ml against an external pressure of 818 mmhg ? express your answer to three significant figures and include the appropriate units.

Answer 1

The gas performs approximately -4680 J of work when it expands from 112 mL to 155 mL against an external pressure of 818 mmHg.

Step-by-step explanation:

To calculate the work done by a gas during expansion against an external pressure, we use the formula W = -PΔV, where W is the work, P is the external pressure, and ΔV is the volume change. It's important to note that the work is negative when the gas does work on the surroundings as it expands.

Firstly, we need to convert the pressure into a consistent unit of measurement. Since 1 mmHg is equal to 133.322 Pa (Pascals), we convert the given pressure:

818 mmHg * 133.322 Pa/mmHg = 109079.396 Pa

Next, we convert the volume change from millilitres to liters:

ΔV = 155 mL - 112 mL = 43 mL = 0.043 L

Now we can calculate the work done:

W = -PΔV = -(109079.396 Pa)(0.043 L)

As 1 L·Pa is equivalent to 1 J, we have:

W = -4684.414 J

Therefore, the gas performs approximately -4680 J (to three significant figures) of work during the expansion. This work is done against an external pressure, and since it's negative, it indicates work done by the gas.

Answer 2

The work done when a gas expands from an initial volume of 112 mL to a final volume of 155 mL against an external pressure of 818 mmHg is 35.174 J.

Step-by-step explanation:

The work done when a gas expands against an external pressure can be calculated using the equation:

Work = External Pressure x Change in Volume

Given:

• Initial volume = 112 mL = 0.112 L
• Final volume = 155 mL = 0.155 L
• External pressure = 818 mmHg

First, convert the volumes to liters:

• Initial volume = 0.112 L
• Final volume = 0.155 L

Then, calculate the change in volume:

• Change in volume = Final volume - Initial volume = 0.155 L - 0.112 L = 0.043 L

Finally, calculate the work:

• Work = External Pressure x Change in Volume = 818 mmHg x 0.043 L = 35.174 J

Therefore, the work done when the gas expands from an initial volume of 112 mL to a final volume of 155 mL against an external pressure of 818 mmHg is 35.174 J.