Question

Suppose that the root-mean-square velocity vrms of water molecules (molecular mass is equal to 18.0 g/mol) in a flame is found to be 1150 m/s. What temperature does this represent

Answer 1

The temperature represented by a root-mean-square velocity of water molecules in a flame can be calculated using the equation vrms = √(3kT/m), where vrms is the velocity, T is the temperature, k is the Boltzmann constant, and m is the molecular mass. Using this equation, the temperature is found to be 8.94 × 10⁵ K.

Step-by-step explanation:

The root-mean-square (vrms) velocity of water molecules in a flame can be used to determine the temperature. The relationship between velocity and temperature is given by the equation vrms = √(3kT/m), where k is the Boltzmann constant (1.38 × 10⁻²³ J/K), T is the temperature in Kelvin, and m is the molecular mass.

In this case, the molecular mass of water (H2O) is 18.0 g/mol. So we can rearrange the equation to solve for the temperature T:

T = (vrms² * m) / (3k)

Substituting the given values, T = (1150 m/s)² * 0.018 kg/mol / (3 * 1.38 × 10⁻²³ J/K) = 8.94 × 10₅ K

T = 464.53 K

Answer 2

`T=954.41\ K`

Step-by-step explanation:

The expression for the root mean square speed is:

`C_(rms)=\sqrt {\frac {3RT}{M}}`

R is Gas constant having value = 8.314 J / K mol

M is the molar mass of gas

Molar mass of water vapor = 18.0 g/mol = 0.018 kg/mol

Temperature = ?

`C_(rms)=1150` m/s

`1150=\sqrt{(3* 8.314* T)/(0.018)}`

`1322500=(24.942T)/(0.018)`

`T=954.41\ K`