Question

calculate rms of SO2at STP
​

Answer 1

Answer:

Root Mean Square Velocity = √ ( 3RT / M )

Here,

• R is universal gas constant
• T is temperature in Kelvin
• M is molar mass is kg

Now Given gas is SO₂

Temperature = Standard Temperature = 273 K

R = 8.314 J / mol.K

Molar mass = 32 + 2 ( 16 )

⇒ Molar mass = 32 + 32 = 64 g = 0.064 kg

Therefore substituting the values in the equation we get,

⇒ V = √ ( 3 × 8.314 × 273 / 0.064 )

⇒ V = √ 106393.2

⇒ V = 326.17 m/s approximately

Hence Root Mean Square Velocity of SO₂ gas is 326.17 m/s

Hope it helped !!

Answer 2

$\huge\red{\bold{\underline{\underline{Solution:-}}}}$

At STP ,

Temperature = 273 K

Molecular weight of SO₂ = 32 + 2(16) = 32 + 32 = 64g = 0.064 kg

R = 8.314 J.atm.mol⁻¹.K⁻¹

$\large\rm\bold{\boxed{{u}_{rms}\:=\:\sqrt{\frac{3RT}{M}}}}$

Where ,

• R is universal gas constant
• M is molecular weight
• T is Temperature

$\large\rm{\rightarrow{{u}_{rms}\:=\:\sqrt{\frac{3(8.314)(273)}{0.064}}}}$

$\large\rm{\rightarrow{{u}_{rms}\:=\:\sqrt{106393.21}}}$

$\large\rm{\rightarrow{{u}_{rms}\:=\:326.17\:m/s}}$

∴ The RMS velocity of SO₂ At STP is 326.17 m/s

$\huge\blue{\bold{\underline{\underline{Additional\:Info:-}}}}$

➣ RMS velocity when Volume , Pressure and Molecular mass are known ,

$\large\rm\bold{\boxed{{u}_{rms}\:=\:\sqrt{\frac{3PV}{M}}}}$

➣ Ratio of RMS velocities of same gas at two different temperatures is given by ,

$\large\rm\bold{\boxed{\frac{u_1}{u_2}\:=\:\sqrt{\frac{T_1}{T_2}}}}$

➣ Ratio of RMS velocities of two different gases at same temperature is given by ,

$\large\rm\bold{\boxed{\frac{u_1}{u_2}\:=\:\sqrt{\frac{M_2}{M_1}}}}$