Homework Answers
Given data
Volume of the Syringe V = 47.5 cc = 4.75 * 10-5 m3
Pressure P = 1.58 atm = 1.58 *1.01 * 105 Pa = 1.59 *105Pa ( 1atm = 1.01 * 105 Pa)
Temperature T = 19.8 oC = (19.8 + 273) K =292.5K
R = 8.314 J/mol-K
Avogadro's number No = 6.022 * 1023 molecules
a) The number of moles in the Syringe
n = PV / RT
=(1.59 * 105 * 4.75 * 10-5 ) / ( 8.314 * 292.5)
= 3.105 * 10-3 moles
Number of Molecules = Number of moles * Avogadro's number
= 3.105 * 10-3 * 6.022 * 1023
= 1.86 * 1021 molecules
Mass of the Air in the Syringe = Number of moles * Molar mass of air
= 3.105*10-3 moles * 28.97 *10-3 Kg/mol
= 8.99 * 10-5 Kg
b) Temperature remains unchanged
Volume after compression Vf = 41.6 cc = 4.1 * 10-5 m3
Pf = ?
PV = Pf Vf
Pf = PV / Vf
= 1.59 * 105 * 4.75 * 10-5 / 4.16 * 10-5
= 1.81 * 105Pa
= 1.81 * 105 / 1.01 *105
= 1.79 atm , 1 atm = 1.01*105 Pa
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