What is the root-means square speed of Sulfur Dioxide gas at 345.0K?

rms = sqrt (3RT/M) where M is molar mass.

what does 3 rt mean?

Try V(rms)= [158 x SqrRt(T/M)]m/s

T = Temp in Kelvin
M = Molecular weight

Vrms = sqrt(3RT/M)

3 = 3
R = 8.314
T = temperature
M = molar mass
All you needed to do is to go to google and type in rms speed molecules.

To calculate the root-mean-square (rms) speed of a gas molecule, you need to use the formula:

v_rms = √(3RT/M)

Where:
v_rms = root-mean-square speed (m/s)
R = gas constant = 8.314 J/(mol·K)
T = temperature in Kelvin (K)
M = molar mass of the gas molecule (kg/mol)

In this case, we need to find the rms speed of Sulfur Dioxide (SO2) gas at 345.0K.

The molar mass of Sulfur Dioxide (SO2) can be calculated using the atomic masses of Sulfur (S) and Oxygen (O).

The atomic mass of Sulfur (S) is approximately 32.07 g/mol, and the atomic mass of Oxygen (O) is approximately 16.00 g/mol.

So, the molar mass of Sulfur Dioxide (SO2) can be calculated as:

M = (molar mass of S) + 2 * (molar mass of O)
= 32.07 g/mol + 2 * 16.00 g/mol
= 32.07 g/mol + 32.00 g/mol
= 64.07 g/mol

Now, we convert the molar mass from grams to kilograms by dividing by 1000:

M = 64.07 g/mol / 1000
= 0.06407 kg/mol

Plugging in the values into the formula, we have:

v_rms = √(3 * R * T / M)
= √(3 * 8.314 J/(mol·K) * 345.0 K / 0.06407 kg/mol)

Simplifying further:

v_rms = √(8.314 * 3 * 345.0 / 0.06407) m/s
= √(85,779.75) m/s
≈ 293.07 m/s

Therefore, the root-mean-square speed of Sulfur Dioxide (SO2) gas at 345.0K is approximately 293.07 m/s.