Answer:
[tex]\large \boxed{\text{0.0820 L$\cdot$atm$\cdot$K$^{-1}$mol}^{-1 }}[/tex]
Explanation:
To solve this problem, we can use the Ideal Gas Law:
pV = nRT
Data:
p = 3.00 atm
V = 17.4 L
n = 2.00 mol
T = 45 °C
Calculations:
1. Convert the temperature to kelvins
T = (45 + 273.15) K = 318.15 K
2. Calculate the value of R
[tex]\begin{array}{rcl}pV & = & nRT\\\text{3.00 atm} \times \text{17.4 L} & = & \text{2.00 mol} \times R \times \text{318.15 K}\\\text{52.2 L$\cdot$atm} & = & 636.30R \text{ K$\cdot$mol}\\R & = & \dfrac{\text{52.2 L$\cdot$atm}}{636.30 \text{ K$\cdot$mol}}\\\\ & = & \textbf{0.0820 L$\cdot$atm$\cdot$K$^{-1}$mol}^{-1} \\\end{array}\\\text{The value of the gas constant R is $\large \boxed{\textbf{0.0820 L$\cdot$atm$\cdot$K$^{-1}$mol}^{-1 }}$}[/tex]
