https://file.aiquickdraw.com/mathbot/file/1726457177121og6jyrnr.jpg

The problem in the image reads as follows:

"A balloon originally has 0.100 moles of helium and has a volume of 0.500 L. If 0.590 grams of He are added to the balloon, what will the new volume be, in L? (Assume temperature and pressure do not change.)"

To solve this, we can use the **Ideal Gas Law**: 
\[
PV = nRT
\]
Since the problem assumes constant temperature and pressure, the ratio of volume to moles should remain constant. Hence, we can use the relation:
\[
\frac{V_1}{n_1} = \frac{V_2}{n_2}
\]

### Given:
- Initial moles of helium: \( n_1 = 0.100 \, \text{mol} \)
- Initial volume: \( V_1 = 0.500 \, \text{L} \)
- Mass of helium added: \( 0.590 \, \text{g} \)
- Molar mass of helium (He): \( 4.0026 \, \text{g/mol} \)

### Steps:
1. Calculate the moles of helium added.
\[
n_{\text{added}} = \frac{0.590 \, \text{g}}{4.0026 \, \text{g/mol}} 
\]
2. Find the total moles of helium after the addition:
\[
n_2 = n_1 + n_{\text{added}}
\]
3. Use the ratio \( \frac{V_1}{n_1} = \frac{V_2}{n_2} \) to solve for the new volume \( V_2 \).

Let's calculate that now.The new volume of the balloon, after adding 0.590 grams of helium, is approximately **1.24 L**.

Would you like further clarification or additional details on the steps involved? Here are some related questions to expand on this topic:

1. What is the Ideal Gas Law and how is it applied in chemistry?
2. How does the molar mass of a gas influence its volume under constant conditions?
3. What assumptions are made when using the Ideal Gas Law in real-world scenarios?
4. How would the volume change if the temperature or pressure were altered?
5. What would happen if you added a different gas with a higher molar mass instead of helium?

**Tip:** Always ensure that the units are consistent when performing gas law calculations, especially when converting between grams, moles, and liters.

A balloon originally has 0.100 moles of helium and has a volume of 0.500 L. If 0.590 grams of He are added to the balloon, what will the new volume be, in L? (Assume temperature and pressure do not change.)

Solve the problem of determining the new volume of a balloon after adding 0.590 grams of helium using the Ideal Gas Law. Learn about mole calculations and gas volume relationships. Ideal for high school chemistry students.

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