QuestionApril 24, 2025

6. A helium balloon has a volume of 3.4 liters and a pressure of 1.05 atmospheres at 25^circ C How many moles of helium gas are in the balloon? How many grams of gas?

6. A helium balloon has a volume of 3.4 liters and a pressure of 1.05 atmospheres at 25^circ C How many moles of helium gas are in the balloon? How many grams of gas?
6. A helium balloon has a volume of 3.4 liters and a pressure of 1.05 atmospheres at 25^circ C How many moles of helium gas are in the balloon? How many grams of gas?

Solution
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Answer

0.145 moles; 0.58 grams Explanation 1. Use Ideal Gas Law The ideal gas law is given by **PV = nRT**. Rearrange to find moles: n = \frac{PV}{RT}. 2. Convert Temperature to Kelvin T = 25 + 273.15 = 298.15 \, K. 3. Calculate Moles of Helium Use P = 1.05 \, atm, V = 3.4 \, L, R = 0.0821 \, \frac{L \cdot atm}{mol \cdot K}. n = \frac{(1.05)(3.4)}{(0.0821)(298.15)} \approx 0.145 \, mol. 4. Calculate Mass of Helium Molar mass of helium is 4.00 \, g/mol. Mass = 0.145 \, mol \times 4.00 \, g/mol = 0.58 \, g.

Explanation

1. Use Ideal Gas Law<br /> The ideal gas law is given by **$PV = nRT$**. Rearrange to find moles: $n = \frac{PV}{RT}$.<br /><br />2. Convert Temperature to Kelvin<br /> $T = 25 + 273.15 = 298.15 \, K$.<br /><br />3. Calculate Moles of Helium<br /> Use $P = 1.05 \, atm$, $V = 3.4 \, L$, $R = 0.0821 \, \frac{L \cdot atm}{mol \cdot K}$.<br /> $n = \frac{(1.05)(3.4)}{(0.0821)(298.15)} \approx 0.145 \, mol$.<br /><br />4. Calculate Mass of Helium<br /> Molar mass of helium is $4.00 \, g/mol$.<br /> Mass = $0.145 \, mol \times 4.00 \, g/mol = 0.58 \, g$.
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