A .25 kg lead ball at a temperature of 85 degree C is placed in an aluminum calo

Question

A .25 kg lead ball at a temperature of 85 degree C is placed in an aluminum calorimeter cup of mass 200 grams. The cup contains 180 grams of water at 22 degree. Find the equilibrium temperature of the system. standard temperature and pressure (STP) is defined as a temperature of 0 degree C and a pressure of 101.3 kPa. What is the volume occupied by one mole of an ideal gas at STP? A ballon contains 3.7 liters of nitrogen gas at 87 degree K and a pressure of 101000 Pa. If the temperature of the gas is allowed to increases 70 degree 24 degree C and the pressure remains constant, what volume will the gas occupy? (Assume the ballon does not leak and the number of moles remains constant.)

Explanation / Answer

4. (a) The volume occupied by one mole of an ideal gas at STP which is given as :

using an ideal gas law, we have

P V = n R T                 

where, R = molar gas constant = 8.314 J/mol.K

n = number of moles = 1

T = temperature = 273.15 K

P = pressure = 101.3 x 103 Pa

then, we get

(101.3 x 103 Pa) V = (1) (8.314 J/mol.K) (273.15 K)

V = (2270.9 J) / (101.3 x 103 Pa)

V = 22.4 x 10-3 m3

V = 22.4 L

(b) Volume of the gas occupied which will be given as :

using a combined gas law, we have

P1 V1 / T1 = P2 V2 / T2

(101000 Pa) (0.0037 m3) / (87 K) = (101000 Pa) V2 / (297 K)

(0.0037 m3) / (87 K) = V2 / (297 K)

V2 = (0.0037 m3) [(297 K) / (87 K)]

V2 = (0.0037 m3) (3.41)

V2 = 0.0126 m3

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