Chemistry Gas/Liquid Volume Question?

Question

You have a plastic syringe attached to a length of Tygon tubing. You carefully set the syringe’s plunger at the 20.0 ml mark and you attach a pressure sensor. The initial pressure reading is 9.87 kPa. You press the plunger until it is precisely at the 6.0 ml mark. The pressure now reads 23.69 kPa. What is the volume of the tubing?

This problem is very confusing for me/ maybe it's the wording. Is the level the syringe set out the volume. If so, we're given volume, and how would we solve for volume?

Any help would be appreciate. Thanks

Answer 1

P1V1 = P2V2



P1 = 9.87 kPa

V1 = Vt + 20.0 mL.. (Vt = volume tubing)

P2 = 23.69 kPa

V2 = Vt + 6.0 mL



*** update ***

sometimes it's easiest to rearrange the equation first and group like terms together so that the units cancel out....watch...



P1V1 = P2V2

V1 = (P2 / P1) x V2

(Vt + 20.0mL) = (P2/P1) x (Vt + 6.0mL)

Vt + 20.0mL = (23.69 kPa / 9.87 kPa) x (Vt + 6.0mL)

Vt + 20.0mL = 2.40 x (Vt + 6.0mL)....notice the units of P1 and P2 drop out?

Vt + 20.0mL = 2.40Vt + 14.4mL

5.6 mL = 1.4Vt

Vt = 5.6 mL / 1.40 = 4.0 mL



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questions?

Answer 2

Apply Boyle-Mariotte law

p1 V1 = p2 V2 = const.

where V1 is net volume of tubing and syringe at first measurement and V2 is volume of tubing and syringe at second measurement. p1 and p2 are measured pressures. If Vt is volume of tubing and Vs1=20ml and Vs2=6ml are volumes of syringe at first and second measurement respectively, then

V1 = Vt + Vs1

V2 = Vt + Vs2

p1 (Vt + Vs1) = p2 (Vt + Vs2)

p1Vs1 - p2Vs2 = Vt (p2 - p1)

Vt = (p1Vs1 - p2Vs2)/(p2 - p1)

Vt = (9870*20*10^-6 - 23690*6*10^-6)/(23690 - 9870)

Vt = (55260/13820) * 10^-6 = 4.0 * 10^-6 m^3 = 4ml



Edit:

In order to simplify calculation, we could convert Pascals to N/cm^2 and ml to cm^3:

1Pa =10^-4 N/cm^2 ( ---> 1kPa = 10^-1 N/cm^2)

1ml = 1cm^3

p1 = 9.87kPa = 0.987 N/cm^2

p2 = 23.69kPa = 2.369 N/cm^2

Vs1= 20ml = 20cm^3

Vs2= 6ml = 6cm^3

Vt = (0.987 * 20 - 2.369 * 6)/(2.369 - 0.987) = 4.0 cm^3 = 4ml

Answer 3

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