Question

At what temperature would 2.10moles of N2 gas have a pressure of 1.25atm and fill a 25.0 L tank

Answer 1

`\large \boxed{\text{-92 $^(\circ)$C}}`

Step-by-step explanation:

We can use the Ideal Gas Law and solve for T.

pV = nRT

Data

p = 1.25 atm

V = 25.0 L

n = 2.10 mol

R = 0.082 06 L·atm·K⁻¹mol⁻¹

Calculations

1. Temperature in kelvins

`\begin{array} {rcl}pV & = & nRT\\\text{1.25 atm} * \text{25.0 L} & = & \rm\text{2.10 mol} * 0.08206 \text{ L}\cdot\text{atm}\cdot\text{K}^(-1)\text{mol}^(-1) * T\\31.25&=&0.09847T\text{ K}^(-1)\\T& = &\frac{31.25}{\text{0.098 47 K}^(-1)}\\\\& = &\text{181 K}\end{array}`

2. Temperature in degrees Celsius

`\begin{array} {rcl}T & = & (181 - 273.15) \, ^(\circ)\text{C}\\& = & -92 \, ^(\circ)\text{C}\\\end{array}\\\text{The temperature of the gas is $\large \boxed{\mathbf{-92 \, ^(\circ)}\textbf{C}}$}`