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Chapter 19: Q20P (page 578)

Question: Calculate the RMS speed of helium atoms at 1000k. Molar mass of helium atoms is $4.0026 \frac{g}{mol}$ .

Short Answer

Expert verified

Answer

The RMS speed of helium atoms at 1000 k is $2.50 \times 10^{3} \frac{m}{s}$ .

Step by step solution

01

Given

The temperature is T = 1000 k

02

Determining the concept

Find the RMS speed from its formula in terms of R, temperature, and molar mass.

Formula is as follow:

$v = \sqrt{\frac{3 R T}{M}}$

Here, M is mass, Tis temperature, v is velocity and R is universal gas constant.

03

Determining the RMS speed of helium atoms at 1000 K

The RMS speed of helium atoms is,

$v = \sqrt{\frac{3 R T}{M}}$

Molar mass of helium is,

$M = 4 \times 10^{- 3} \frac{kg}{mol}$

Substitute the values in the equation for velocity and solve as:

$v = \sqrt{\frac{3 (8.314) (1000)}{4 \times 10^{- 3}}} v = 2497 \approx 2.50 \times 10^{3} \frac{m}{s}$

Hence, the RMS speed of helium atoms at 1000 K is $2.50 \times 10^{3} \frac{m}{s}$ .

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Most popular questions from this chapter

It is found that the most probable speed of molecules in a gas when it has (uniform) temperature $T_{2}$ is the same as the RMS speed of the molecules in this gas when it has (uniform) temperature, $T_{1}$ . Calculate $T_{2} / T_{1}$ .

At what temperature does the rms speed of

a) $H_{2}$ (Molecular hydrogen)

b) $O_{2}$ (Molecular oxygen)

equal the escape speed from Earth?

At what temperature does the rms speed of

c) $H_{2}$ (Molecular hydrogen)

d) $O_{2}$ (Molecular oxygen) equal the escape speed from the Moon (where the gravitational acceleration at the surface has magnitude )?

Considering the answers to parts (a) and (b), should there be much

e) Hydrogen

f) Oxygen high in Earth’s upper atmosphere, where the temperature is about $1000 K$ ?

(a) What is the number of molecules per cubic meter in air at $20 ° C$ and at a pressure of $1.0 atm (= 1.01 \times 10^{5} Pa) ?$

(b) What is the mass of $1.0 m^{3}$ of this air? Assume that 75% of the molecules are nitrogen ( $N_{2}$ ) and 25% are oxygen ( $O_{2}$ ).

In a certain particle accelerator, protons travel around a circular path of diameter $23.0 m$ in an evacuated chamber, whose residual gas is at $295 K$ and $1.00 \times 10^{- 6} t o r r$ pressure.

Calculate the number of gas molecules per cubic centimeter at this pressure.
What is the mean free path of the gas molecules if the molecular diameter is $2.00 \times 10^{- 8} c m$ ?

A container holds a mixture of three non reacting gases: $2.40 m o l$ of gas 1 with $C_{V 1} = 12.0 J / (m o l . K)$ , $1.50 m o l$ of gas 2 with $C_{V 2} = J / (m o l . K)$ andof gas 3 with $C_{V 3} = 20.0 J / (m o l . K)$ . What is $C_{V}$ of the mixture?

See all solutions

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