Final answer:
To find the root mean square speed of a gas at 113°C with a molar mass of 28.01 g/mol, first convert the temperature to Kelvin and the molar mass to kg/mol. Then use the root mean square speed formula with the gas constant. Lastly, calculate the value to get the speed in meters per second.
Step-by-step explanation:
The student has asked to calculate the root mean square speed (urms) of molecules in a gas sample at 113°C, with a molar mass of 28.01 g/mol. First, convert the given temperature to Kelvin by adding 273 to the Celsius temperature: 113°C + 273 = 386 K. Also, convert the molar mass to kilograms per mole for consistency in SI units: 28.01 g/mol × (1 kg / 1000 g) = 0.02801 kg/mol. Next, use the formula:
urms = √(3RT/M),
where R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and M is the molar mass in kg/mol. Plugging in the values, we get:
urms = √[(3)(8.314 J/mol·K)(386 K) / 0.02801 kg/mol]
Calculating the above expression, we can find the root mean square speed in meters per second. This provides an estimation of the average speed a given molecule in the gas sample might have, which is pertinent for understanding gas behavior.