(b) Calculate the rms speed of NF 3 molecules at 25 °C.

Identify the formula for the root mean square (rms) speed: $$ v_{\text{rms}} = \sqrt{\frac{3RT}{M}} $$, where $$ R is $$the ideal gas constant, $$ T is $$the temperature in Kelvin, and $$ M is $$the molar mass in kg/mol.. Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.. Determine the molar mass of NF_{3} by adding the atomic masses of nitrogen (N) and fluorine (F) from the periodic table: $$ M = M_N + 3 \times M_F .. $$Convert the molar mass from grams per mole to kilograms per mole by dividing by 1000.. Substitute the values of $$ R $$, $$ T $$, and $$ M $$ into the rms speed formula and solve for $$ v_{\text{rms}} .$$

(b) Calculate the rms speed of NF3 molecules at 25 °C.

Identify the formula for the root mean square (rms) speed: $$ v_{\text{rms}} = \sqrt{\frac{3RT}{M}} $$, where $$ R is $$the ideal gas constant, $$ T is $$the temperature in Kelvin, and $$ M is $$the molar mass in kg/mol. Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. Determine the molar mass of NF_{3} by adding the atomic masses of nitrogen (N) and fluorine (F) from the periodic table: $$ M = M_N + 3 \times M_F . $$Convert the molar mass from grams per mole to kilograms per mole by dividing by 1000. Substitute the values of $$ R $$, $$ T $$, and $$ M $$ into the rms speed formula and solve for $$ v_{\text{rms}} .$$

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

문제 81b

10장, 문제 81b

(b) Calculate the rms speed of NF₃ molecules at 25 °C.

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Identify the formula for the root mean square (rms) speed: $ v_{\text{rms}} = \sqrt{\frac{3RT}{M}} $, where $ R $ is the ideal gas constant, $ T $ is the temperature in Kelvin, and $ M $ is the molar mass in kg/mol.

Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Determine the molar mass of NF₃ by adding the atomic masses of nitrogen (N) and fluorine (F) from the periodic table: $ M = M_N + 3 \times M_F $.

Convert the molar mass from grams per mole to kilograms per mole by dividing by 1000.

Substitute the values of $ R $, $ T $, and $ M $ into the rms speed formula and solve for $ v_{\text{rms}} $.

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주요 개념

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Root Mean Square (RMS) Speed

The root mean square speed is a measure of the average speed of particles in a gas. It is calculated using the formula v_rms = sqrt(3RT/M), where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas in kg/mol. This concept is crucial for understanding the kinetic energy and behavior of gas molecules.

Ideal Gas Law

The ideal gas law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law assumes that gas molecules do not interact and occupy no volume, which simplifies calculations involving gas properties. Understanding this law is essential for deriving the RMS speed in the context of gas behavior.

Temperature Conversion

Temperature must be expressed in Kelvin for calculations in thermodynamics and gas laws. To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. This conversion is necessary when calculating RMS speed, as the temperature directly influences the kinetic energy and speed of gas molecules.