Chapter 20: Q. 17 (page 567)

At what temperature $(i n ° C)$ do hydrogen molecules have the same $r m s$ speed as nitrogen molecules at $100 ° C$ ?

Short Answer

Expert verified

The temperature of hydrogen molecules is $- 246 ° C$

Step by step solution

Introduction

Equating the expressions for the $r m s$ speeds, we can find

$\sqrt{\frac{3 k_{B} T_{n}}{m_{n}}} = \sqrt{\frac{3 k_{B} T_{h}}{m_{h}}}$

We can simplify the constants and raise the expression to the second power, thus obtaining

$\frac{T_{n}}{m_{n}} = \frac{T_{h}}{m_{h}}$

It is therefore clear that the temperature of the hydrogen molecules will be

$T_{h} = T_{n} \frac{m_{h}}{m_{n}}$

Substitution

Let us remember that the mass $m$ of a molecule of a substance with molar mass $M$ will be

$m = \frac{M}{N_{A}}$

Therefore it is clear that the ratio of molecular masses will be that of the molar masses,

$\frac{m_{h}}{m_{n}} = \frac{M_{h}}{M_{n}}$

Our final expression therefore becomes

$T_{h} = T_{n} \frac{M_{h}}{M_{n}}$

Numerically we will have

$T_{h} = (100 + 273) \frac{2}{28} \approx \underline{27 K}$

In degrees Celsius, this temperature belongs to $- 246 ° C$

Step 3:The Value of temperature

The temperature belongs to $- 246 ° C$

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At what temperature $(i n ° C)$ do hydrogen molecules have the same $r m s$ speed as nitrogen molecules at $100 ° C$ ?

Short Answer

Step by step solution

Introduction

Substitution

Step 3:The Value of temperature

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At what temperature (in°C)do hydrogen molecules have the same rms speed as nitrogen molecules at 100°C ?

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Substitution

Step 3:The Value of temperature

One App. One Place for Learning.

Most popular questions from this chapter

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At what temperature $(i n ° C)$ do hydrogen molecules have the same $r m s$ speed as nitrogen molecules at $100 ° C$ ?