Answer to Question #190515 in General Chemistry for Adrionna

Question

11.  A gas storage tank as a volume of 4.5x10⁵ m³ at 29 °C and 101.3 kPa.  What is the new volume in cubic meters of the tank if the temperature drops to -15 °C and the pressure drops to 86 kPa? 

Answer 1

Case 1:

$P=101.3kpa, V=4.5\times 10^5m^3, T=302K$

Using Ideal gas Equation-

$PV=nRT \\[9pt] 101.3\times 10^5\times 4.5\times 10^5=nR\times 302\\[9pt] \Rightarrow nR=1.509\times 10^{10} ~~~~~~=(1)$

Case 2:

$P=86kpa,T=258K,$

Using Ideal gas equation again-

$PV=nRT \\[9pt] 86\times 10^5\times V=1.509\times 10^{10}\times 258\\[9pt]V=\dfrac{389.43}{86}\times 10^5 \\[9pt]=4.528\times 10^5 m^3$