Final answer:
To find the mass of a single molecule given its RMS speed, we use the kinetic energy equation relating temperature, speed, and mass. The temperature is first converted to Kelvin, and the mass is calculated by rearranging the kinetic energy equation. However, the calculated mass does not match the provided options, indicating a potential error.
Step-by-step explanation:
To calculate the mass (m) of a single molecule in the gas, we can use the formula for root-mean-square (RMS) speed of a molecule in an ideal gas, which is related to the kinetic energy (KE). The kinetic energy of a molecule with mass m moving at RMS speed v is given by KE = 1/2 m v². This is equal to 3/2 kT, where k is the Boltzmann constant and T is the temperature in Kelvin. From the provided RMS speed and temperature, we can rearrange this equation to solve for the mass of a single molecule:
The formula to be used is:
KE = 1/2 m v² = 3/2 kT
First, we convert 141°C to Kelvin by adding 273.15 to get 414.15 K. Substituting the values and solving for m we get:
m = (3 k T)/(v²)
Inserting the Boltzmann constant k = 1.38 × 10⁻²³ J/K, temperature T = 414.15 K, and velocity v = 195 m/s, we can calculate the mass of the molecule in kg. After performing the calculations, we find that the mass of a single molecule is 4.65 × 10⁻²¶ kg, which is not an exact match to any of the options provided, suggesting a possible error in either the information given or the options available.