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The given problem asks how many times the pressure of a rarefied monoatomic gas will change if:

- The absolute temperature of the gas is halved.
- The concentration of molecules is doubled.

To solve this, we can use the ideal gas law in the form:

\[
P = nkT
\]

where:
- \( P \) is the pressure,
- \( n \) is the concentration of molecules (number of particles per unit volume),
- \( k \) is the Boltzmann constant,
- \( T \) is the absolute temperature.

### Step-by-step solution:

1. The pressure \( P \) is directly proportional to both the concentration \( n \) and the temperature \( T \).
   
2. If the concentration \( n \) increases by a factor of 2, the pressure will also increase by a factor of 2.

3. If the temperature \( T \) decreases by a factor of 2, the pressure will decrease by a factor of 2 as well.

Now we combine the effects:
- Doubling \( n \) increases the pressure by a factor of 2.
- Halving \( T \) decreases the pressure by a factor of 2.

Thus, the combined effect is:

\[
P_{\text{new}} = \frac{2P}{2} = P
\]

So, the pressure remains the same and does **not change**.

### Answer:
The pressure does not change, or it changes by a factor of **1**.

Let me know if you'd like further clarification or details on the solution! Here are some related questions to deepen your understanding:

1. What would happen to the pressure if the temperature was tripled instead?
2. How does the ideal gas law change if the gas is not monoatomic but diatomic?
3. What are the conditions where the ideal gas law may no longer apply?
4. How would the pressure change if the concentration and temperature were both halved?
5. What is the physical meaning of the Boltzmann constant in the ideal gas equation?

**Tip:** Always keep track of how variables like temperature, volume, and concentration affect pressure by thinking of their relationships through the ideal gas law!

Во сколько раз изменится давление разреженного одноатомного газа, если абсолютная температура газа уменьшится в 2 раза, а концентрация молекул увеличится в 2 раза?

Learn how the pressure of a rarefied monoatomic gas changes when the temperature is halved and the concentration of molecules doubles. This problem involves the ideal gas law and provides a step-by-step solution for physics students.

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