calculate the root mean square velocity and average velocity for oxygen molecules of 0°C
Answers
Answer:
Answer
27
∘
C=300 K
Root mean square speed =
M
3RT
R=8.314×10
7
erg K
−1
mol
−1
;M=32 g mol
−1
;T=300 K
Substituting the values,
=
32
3×8.314×10
7
×300
=483.56 cm/sec
=483.56 m/sec
Average speed =
πM
8RT
=
22×32
8×8.314×10
7
×300×7
=445.42 cm/sec
=445.42 m/sec
Most probable speed =
M
2×R×T
=
32
2×8.314×10
7
×300
=39482 cm/sec
=394.83 m/sec.
Step-by-step explanation:
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The average velocity or root mean square velocity of a molecule in a sample of oxygen at 0 degrees Celsius is 461 m/sec.
Explanation:
Gases consist of atoms or molecules that move at different speeds in random directions. The root mean square velocity (RMS velocity) is a way to find a single velocity value for the particles. The average velocity of gas particles is found using the root mean square velocity formula:
μrms = (3RT/M)½
μrms = root mean square velocity in m/sec
R = ideal gas constant = 8.3145 (kg·m2/sec2)/K·mol
T = absolute temperature in Kelvin
M = mass of a mole of the gas in kilograms.
Really, the RMS calculation gives you root mean square speed, not velocity. This is because velocity is a vector quantity that has magnitude and direction. The RMS calculation only gives the magnitude or speed. The temperature must be converted to Kelvin and the molar mass must be found in kg to complete this problem.
Step 1
Find the absolute temperature using the Celsius to Kelvin conversion formula:
T = °C + 273
T = 0 + 273
T = 273 K
Step 2
Find molar mass in kg:
From the periodic table, the molar mass of oxygen = 16 g/mol.
Oxygen gas (O2) is comprised of two oxygen atoms bonded together. Therefore:
molar mass of O2 = 2 x 16
molar mass of O2 = 32 g/mol
Convert this to kg/mol:
molar mass of O2 = 32 g/mol x 1 kg/1000 g
molar mass of O2 = 3.2 x 10-2 kg/mol
Step 3
Find μrms:
μrms = (3RT/M)½
μrms = [3(8.3145 (kg·m2/sec2)/K·mol)(273 K)/3.2 x 10-2 kg/mol]½
μrms = (2.128 x 105 m2/sec2)½
μrms = 461 m/sec
∴The average velocity or root mean square velocity of a molecule in a sample of oxygen at 0 degrees Celsius is 461 m/sec.