Question

if 8.85 moles of carbon monoxide gas are present in a container of volume 34.71 l, what is the pressure of the gas, in atm, if the temperature is 97°c? report your answer using the appropriate number of significant figures.
r = 0.0821 (\frac{lcdot atm}{molcdot k}) or 8.314 (\frac{kpacdot l}{molcdot k})

Explanation:

Step1: Convert temperature to Kelvin

The temperature is given in Celsius, so we convert it to Kelvin using the formula \( T(K) = T(^\circ C) + 273.15 \).
\( T = 97 + 273.15 = 370.15 \, K \)

Step2: Use the Ideal Gas Law

The Ideal Gas Law is \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the gas constant, and \( T \) is temperature. We need to solve for \( P \), so rearrange the formula: \( P = \frac{nRT}{V} \)

Given:
\( n = 8.85 \, mol \)
\( R = 0.0821 \, \frac{L \cdot atm}{mol \cdot K} \) (since we want pressure in atm)
\( T = 370.15 \, K \)
\( V = 34.71 \, L \)

Substitute the values into the formula:
\( P = \frac{8.85 \, mol \times 0.0821 \, \frac{L \cdot atm}{mol \cdot K} \times 370.15 \, K}{34.71 \, L} \)

Step3: Calculate the numerator

First, calculate the numerator: \( 8.85 \times 0.0821 \times 370.15 \)
\( 8.85 \times 0.0821 \approx 0.726585 \)
\( 0.726585 \times 370.15 \approx 268.9 \)

Step4: Calculate the pressure

Now divide by the volume: \( P = \frac{268.9}{34.71} \approx 7.75 \, atm \)

Answer:

\( 7.75 \, atm \) (rounded to three significant figures, as the given values have three or four significant figures, and 8.85 has three, so the answer should have three)