A balloon holds 2.20 L of helium at 20 C and atmospheric pressure. (a) How many

Question

A balloon holds 2.20 L of helium at 20 C and atmospheric pressure.

(a) How many moles of helium are in the balloon?

(b) The balloon is taken outside, and its volume shrinks to 1.95 L. What is the temperature outside (in C)? Assume no helium leaks from the balloon.

(c) The balloon is taken back inside and allowed to return to its original volume and 20 C. It is then compressed back to 1.95 L. Assuming its temperature remains at 20 C and no helium escapes, what is the final pressure of the balloon?

Equations:
PV=nRT
R=8.31 J/(mol?K)
TK=TC+273.15

Explanation / Answer

a), given volume V = 2.2 litre = 2.2 x 10-3 m3 ; pressure P = 1atm = 101325 Pa

temperature T = 200 C = 20 + 273 = 293 K

following PV = nRT we get number of moles n = PV/RT = 101325 x 2.2 x 10-3/ 8.31 x 293

= 91.55 x 10-3

b) here V = 1.95 x 10-3 m3 therefore temperature T = PV / nR = 101325 x 2.2 x 10-3 /91.55 x 10-3 x 8.31 = 293K =293 - 273 =200 C

c) here V1 = 2.20 x 10-3 m3 ; V2 = 1.95 x 10-3 m3 ; P1 = 101325 Pa ; P2 = ? temperature is constant hence P1V1 = P2V2 or P2 = P1V1 / V2 = 101325 x 2.2 x 10-3 / 1.95 x 10-3

= 114315.38 Pa

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