Question

suppose that the rms speed of carbon dioxide molecules, with molar mass of 44.0 g/mol, in a flame is found to be 0.95 × 105 m/s.

Answer 1

The question asks for the temperature corresponding to the given rms speed of carbon dioxide molecules, which can be solved by applying the formula for rms speed in an ideal gas and rearranging the equation to solve for temperature in Kelvin.

Step-by-step explanation:

The question involves the concept of the root-mean-square (rms) speed of gas molecules, which is a topic in Physics, specifically in the area of thermodynamics and kinetic theory. To find the temperature that corresponds to the given rms speed for a molecule with a known molar mass, we would use the formula:

Urms = \(\sqrt{(3k_BT/M)}\)

Where Urms is the root-mean-square speed, k_B is Boltzmann's constant (1.38 \(\times\) 10-23 J/K), T is the temperature in Kelvin, and M is the molar mass in kilograms per mole.

To find T, we rearrange the equation to:

T = \(\frac{M \cdot Urms^2}{3k_B}\)

First, we convert the molar mass of carbon dioxide from grams per mole to kilograms per mole:

M = 44.0 g/mol \(\times\) 1 kg/1000 g = 0.044 kg/mol

Next, we can plug the known values into our rearranged equation:

T = \(\frac{0.044 kg/mol \cdot (1.05 \(\times\) 10^5 m/s)^2}{3 \cdot 1.38 \(\times\) 10^{-23} J/K}\)

Upon solving, this will give us the temperature in Kelvin. Remember to use appropriate significant figures based on the given data.

Answer 2

The question asks for the calculation of the temperature of a carbon dioxide gas sample given its rms speed. This is a kinetic theory of gases problem in physics, and involves rearranging the ideal gas equation to solve for temperature using the provided rms speed and molar mass of CO2.

Step-by-step explanation:

The question involves using the root-mean-square (rms speed) of carbon dioxide molecules to find the corresponding temperature of the gas. According to the kinetic theory of gases, the rms speed (Urms) is associated with the temperature of the gas through the equation for an ideal gas, which can be written as Urms = √(3kBT/m) where 'kB' is the Boltzmann constant, 'T' is the temperature in kelvins, and 'm' is the mass of one molecule of the gas. The molar mass of the gas needs to be converted to the mass of one molecule by dividing by Avogadro's number.

Calculation Steps:

Convert molar mass of CO2 (44.0 g/mol) to kg to obtain the mass of one molecule in kg by dividing by Avogadro's number (6.022 × 10²23 mol−1).

Use the given Urms (1.05 × 10²5 m/s) and the molecular mass to solve for 'T' using the aforementioned equation.

The temperature can then be determined by rearranging the equation: T = m∙Urms²/(3kB).