Question

The number of oxygen molecules in a cylinder of volume 1m3 at temperature 327C and pressure 27.6 Pascal is= ?

40 points!

Answer 1

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The number of oxygen molecules in a cylinder of volume 1m3 at temperature 327C and pressure 27.6 Pascal is= ?

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Given,

Pressure, P=13.8Pa

Temperature, T=(27+273.15)K

Volume V=1 m 3 Boltzman constant k B =1.38×10−23 JK −1R

universa =N A K B

=(6.023×10 23 )×(1.38×10 −23 )=8.314 J/mol

Apply Ideal gas equationPV=nRT

n= RTPV

= 8.314(27+273.15)13.8×1

=5.53×10 −3 mol

x=n×N A

=(5.53×10 −3 )×(6.023×10 +23 )=3.33×10 21

molecules

Number of molecules is 3.33×10 21

Answer 2

Given:-

• Volume = V = 1 m³
• Temperature = T = 327 °C
• Pressure = 27.6 Pa

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Need to find:-

• Number of molecules of Oxygen = ?

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Solution:-

→ Temperature

= 327°C

= 327 + 273 K

= 600K

We know from IDEAL GAS EQUATION that:

PV = nRT

Where,

• P = Pressure
• V = Volume
• n = Number of moles
• R = Gas Constant = 25/3
• T = Temperature (always in Kelvin)

Substitute the values:-

→ 27.6 × 1 = n × 25/3 × 600

→ 27.6 = n × 25 × 200

→ n = 27.6 ÷ (25 × 200) moles

→ n = 27.6 ÷ 5000 moles

→ n = 5.52 × 10⁻³ moles

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Number of Molecules:

= Number of moles × Avogardo's Number

= 5.52 × 10⁻³ × 6.022 × 10²³

= 33.24 × 10²⁰ (ans)

⋆ There will be 33.24 × 10²⁰ molecules of Oxygen.