General Knowledge - Chemistry - Discussion

Let's solve it step- by- step:

Formula for molecular speed ( root mean square speed, urms):

Urms=√3RT/M

R=universal gas constant.
T= temperature in Kelvin.
M= molar mass (in kg/mol).

Higher t/m-higher speed. So we need to compare T/M for each gas.

Given:

A. H2 at -73⁰C _T= -73+273=200 k,M(H2)=2 g/mol = 0.002 kg/mol.
B. CH4 at 300 K_M(CH4) = 16 g/mol = 0.016 kg/mol,
C. N2 at 1,027⁰C_T=1,027 + 273 = 1300 k, M(N2) = 28 g/mol = 0.028 kg/mol,
D. O2 at 0⁰C_T=0 + 273 = 273K, M(02) = 32 g/mol = 0.032 kg /mol.

Now calculate T/M roughly:

A: 200/0.002 = 100,000.
B: 300/0.016 = 1 8,750.
C.1300/0.028 = 46,429.
D.273/0.032 = 8,531.

Result

Highest value is 100,000 for A(H2 at -73⁰C).

Thus, the Answer: A. H2 at -73⁰C.

CH4 IS THE ANSWER TO THE QUESTION BECAUSE.

Average speed = Square root of (8RT/pi M).

T = Temperature.

Pi = 22/7 or 3.14.

M = molecular mass.

Now since mass is in denominator. It means molecular mass is inversely proportional to average speed. So as mass increases average speed decreases. And as mass decreases average speed increases.

So find out which of the following has lightest molecular mass?

CH4 = 16 g/mole.

Kr = 83.8 g/mole.

N2 = 28 g/mole.

CO2 = 44 g/mole.

Ar = 39.9 g/mole.

Since CH4 has lowest molecular mass among these so it's average speed will be highest.

Its not like that.

The speed of gas is calculated by a relation.

Root Mean square velocity µ(rms) = (3RT/M).

From this relation we can calculate speed.

Only mass could not be taken into consideration here because temperature is specified.

So after calculation.

Speed of Hydrogen gas = 157380 unit.

Speed of Methane gas = 68385 unit.

Speed of Nitrogen gas = 142356 unit.

Speed of oxygen gas = 46128 unit.

If they were all of equal mass and temperature then yes H2.

However according to collision theory, the higher the temperature, the more kinetic energy each particle will have and therefore more collisions occur producing products.

The closer to zero Kelvin, the less energy a particle has (at 0K particles have 0 kinetic energy).

The only correct answer would be C.

K.E directly prop.to Temperature. So at this point of view C is correct but According to Graham's law Rate of effusion of a gas is inversely proportional to the square root of the molar mass of its particles so H is very small molar mass in Periodic Table 1.006 somehow, and N is 14. So the correct answer is A.

I agree with @Jeffrin.

V is directly proportional to T.

With the decrease in temperature, attraction between the hydrogen molecules take place which will limit the movements of particles. This leads to decrease in kinetic energy which results in less speed of molecules. Thus, option A is incorrect.

By considering RMS velocity equation, speed of the molecule depends on both the factors i.e.Temp. & Molar mass equally. By calculating the RMS values hydrogen will give more value of RMS.

Hence hydrogen will have highest speed at that temp. Than rest molecules given above.

According to kinetic theory of gases. Rms velocity of a gas= square root of 3RT/M. Therefore speed of a gas is proportional to under root of T/M where t is temp in kelvin and m is molar mass. Calculating this value we get hydrogen has highest speed.

Guys, please take a closer look in option A.

The temp is of a negative sign (-73).

All of us knows that the speed of the gas is directly proportional to temp.

If the temp is very low then how can the speed increase even though it has a low mass?

A is correct because its mass is negligible and other gases have some mass more than hydrogen when their temperature is divided and find square root their value is very less as compared to hydrogen case so no doubt that H will have more speed.