https://file.aiquickdraw.com/mathbot/file/1726104019904ur3sfrti.jpg

The image describes a typical gas law problem that involves changes in pressure and temperature for an ideal gas. In this case, the ideal gas law equation is used in its combined form to relate the initial and final states of a gas:

\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\]

### Given:
- Initial volume \( V_1 = 30.0 \, \text{mL} \)
- Initial temperature \( T_1 = 20^\circ \text{C} = 273 + 20 = 293 \, \text{K} \)
- Initial pressure \( P_1 = 740 \, \text{mmHg} \)
- Final temperature \( T_2 = 0^\circ \text{C} = 273 \, \text{K} \)
- Final pressure \( P_2 = 760 \, \text{mmHg} \)
- Final volume \( V_2 \) (this is what we need to find).

### Solution:
From the equation:
\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\]

Substitute the known values:
\[
\frac{740 \times 30.0}{293} = \frac{760 \times V_2}{273}
\]

This simplifies to:
\[
\frac{22200}{293} = \frac{760 \times V_2}{273}
\]

\[
75.77 = \frac{760 \times V_2}{273}
\]

Now, solve for \( V_2 \):
\[
75.77 \times 273 = 760 \times V_2
\]
\[
20678.21 = 760 \times V_2
\]
\[
V_2 = \frac{20678.21}{760} = 27.22 \, \text{mL}
\]

Thus, the final volume \( V_2 \) is approximately **27.2 mL**.

Would you like a detailed explanation of any part of this solution? 

Here are 5 related questions you might want to explore:
1. How does the ideal gas law account for changes in volume when only temperature changes?
2. What would happen if the temperature of the gas was further lowered below \( 0^\circ C \)?
3. How does atmospheric pressure influence gas volume calculations?
4. What are the assumptions behind the ideal gas law, and when might they fail?
5. Can the ideal gas law be applied to real gases under all conditions?

**Tip:** When working with gas law problems, always ensure temperatures are in Kelvin (K), not Celsius (°C).

In the assay of ethyl nitrite spirit, the nitric oxide gas liberated from a definite quantity of spirit occupies a volume of 30.0 mL at 20°C and 740 mm Hg. Assuming the gas is ideal, what is the volume at 0°C and 760 mm Hg?

Learn how to calculate the change in volume of nitric oxide gas when temperature and pressure change using the Ideal Gas Law. This problem involves understanding the relationship between pressure, volume, and temperature for an ideal gas. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation