Question

For the gas constant, use R = 8.314 J/mol-K For Avogadro's number, use N_0 = 6.022 times 10^23 molecules. Be careful of units! All the conversions you need are in the information section of the lab. Suppose the volume of the syringe is 47.5 cc. You measure the pressure as 1.58 atm, and the temperature as 19.8 degree C. Assume: the diameter of the plunger on the syringe is 1.44 cm. Find the number of moles of gas in the syringe n = moles the number of molecules of gas in the syringe. N = molecules the mass of air in the syringe. (Use the molar mass of air given in the information section of the lab.) m_air = kg Supose you push down the syringe so the volume is now 41.6 cc, with the temperature remaining unchanged. Find: the new pressure inside the syringe. P = atm the magnitude of the force exerted by the gas on the plunger of the syringe. F = N Suppose you suddenly press down on the syringe so the volume is now 19.2 cc, and plunge it into cold water. When the temperature is 4.06 percentage C, find the pressure inside the syringe. P = atm

Answer 1

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 N_o = 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 V_f = 41.6 cc = 4.1 * 10^-5 m³

P_f = ?

   PV = P_f V_f

P_f = PV / V_f

   = 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