Question

Calculate rms velocity of chlorine molecule at 15 c and 75cmhg pressure

Answer 1

Answer:

Temperature, T1 = 15℃ = 15+273 = 288 K

Pressure, P1 = 75 cmHg = 0.986 atm

Molar mass of chlorine molecule, M  = 70.90 g/mol

The Vrms of the chlorine molecule can be found by two methods:

Method 1:

At NTP conditions, we have  

Pressure, P2 = 1 atm

Temperature, T2 = 273 K

Volume, V2 = 22.4 L

The Ideal Gas Law gives,

PV = nRT

Since n & R is constant

Therefore,  

P1V1/T1 = P2V2/T2

⇒ V1 =  [P2V2/T2] * [T1/P1]

⇒ V1 = [1 * 22.4 / 273] * [288 / 0.986] = 23.96 L

Now,  

The rms velocity of chlorine is given as,

= √[3PV/M]

= √[3* 0.986 * 23.96/70.90] …. [substituting the given values]

= √[0.999]

= 0.999

≈ 1 m/s

Method 2:

Another formula for finding the rms velocity of the chlorine molecule is,

= √[3RT/M]

= √[3* 0.0821 * 288/70.90] …. [substituting the given values and taking R = 0.0821 LatmK⁻¹mol⁻¹]

= √[3* 0.0821 * 288/70.90]

= 1 m/s