Multiple Choice
A 0.334 g sample of an unknown halogen occupies 109 mL at 398 K and 1.41 atm. What is the identity of the halogen?
7. Gases
The Ideal Gas Law
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A capsule of gas has a volume of 550 L, a pressure of 1750 atm, and a temperature of 7500 degrees Celsius. It is broken, releasing the gas into an environment at STP. How many moles of gas are there in the capsule?
A
1.75 moles
B
4.00 moles
C
3.50 moles
D
0.25 moles
Verified step by step guidance1
First, convert the temperature from degrees Celsius to Kelvin. The formula for conversion is: \( T(K) = T(°C) + 273.15 \).
Next, use the Ideal Gas Law to find the number of moles of gas in the capsule. The Ideal Gas Law is given by: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin.
Substitute the known values into the Ideal Gas Law equation. Use \( P = 1750 \) atm, \( V = 550 \) L, \( T \) in Kelvin from step 1, and \( R = 0.0821 \) L·atm/(mol·K), which is the ideal gas constant.
Rearrange the equation to solve for \( n \), the number of moles: \( n = \frac{PV}{RT} \).
Calculate \( n \) using the rearranged equation from step 4, ensuring all units are consistent, particularly the temperature in Kelvin and pressure in atm.
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