Question

part c
a240: l kiln is used for vitrifying ceramics. it is currently operating at 875 °c, and the pressure is 0.9000 atm. how many moles of air molecules are within the confines of the kiln?
express your answer to three significant figures and include the appropriate units.
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part d
a 16.0 l gas cylinder has been filled with 6.60 moles of gas. you measure the pressure to be 3.30 atm. what is the temperature inside the tank?
express your answer to three significant figures and include the appropriate units.
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Explanation:

Step1: Identify the gas law

We use the ideal gas law, \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the gas constant (\( 0.0821 \, \text{L·atm/(mol·K)} \)), and \( T \) is temperature in Kelvin. First, convert temperature from Celsius to Kelvin: \( T = 875 + 273.15 = 1148.15 \, \text{K} \).

Step2: Rearrange the ideal gas law to solve for \( n \)

From \( PV = nRT \), we get \( n = \frac{PV}{RT} \).

Step3: Substitute the values

Given \( P = 0.9000 \, \text{atm} \), \( V = 240 \, \text{L} \), \( R = 0.0821 \, \text{L·atm/(mol·K)} \), \( T = 1148.15 \, \text{K} \). Plugging in: \( n = \frac{0.9000 \times 240}{0.0821 \times 1148.15} \).

Step4: Calculate the numerator and denominator

Numerator: \( 0.9000 \times 240 = 216 \). Denominator: \( 0.0821 \times 1148.15 \approx 94.26 \). Then \( n = \frac{216}{94.26} \approx 2.29 \).

Answer:

\( 2.29 \, \text{mol} \)