Question

a gas occupies 5,020 ml when held at 91 °c and 1.7 atm. how many moles of gas are present? report your answer to 2 places after the decimal point. r = 0.0821 \frac{l \cdot atm}{mol \cdot k}

Explanation:

Step1: Convert units

Convert volume from mL to L: \( 5020\space mL = 5020\div1000 = 5.020\space L \)
Convert temperature from \( ^\circ C \) to K: \( T = 91 + 273.15 = 364.15\space K \)

Step2: Use Ideal Gas Law

The Ideal Gas Law is \( PV = nRT \), solve for \( n \): \( n=\frac{PV}{RT} \)
Substitute values: \( P = 1.7\space atm \), \( V = 5.020\space L \), \( R = 0.0821\frac{L\cdot atm}{mol\cdot K} \), \( T = 364.15\space K \)
\( n=\frac{1.7\times5.020}{0.0821\times364.15} \)
Calculate numerator: \( 1.7\times5.020 = 8.534 \)
Calculate denominator: \( 0.0821\times364.15 \approx 29.90 \)
\( n=\frac{8.534}{29.90} \approx 0.2854 \)
Round to 2 decimal places: \( n \approx 0.29 \)

Answer:

\( 0.29 \)