type the correct answer in the box. express your answer to three significant figures. an empty water bottle…

type the correct answer in the box. express your answer to three significant figures. an empty water bottle is full of air at 15°c and standard pressure. the volume of the bottle is 0.500 liter. how many moles of air are in the bottle? the water bottle contains mole of air.

type the correct answer in the box. express your answer to three significant figures. an empty water bottle is full of air at 15°c and standard pressure. the volume of the bottle is 0.500 liter. how many moles of air are in the bottle? the water bottle contains mole of air.

Answer

Answer:

$2.04\times 10^{-2}$ mol

Explanation:

Step1: Convert temperature to Kelvin

$T=(15 + 273.15)\text{ K}=288.15\text{ K}$

Step2: Identify standard - pressure value

$P = 1\text{ atm}=101325\text{ Pa}$

Step3: Convert volume to SI unit

$V = 0.500\text{ L}=0.500\times10^{- 3}\text{ m}^3$

Step4: Use ideal gas law $PV = nRT$

$n=\frac{PV}{RT}$, where $R = 8.314\text{ J/(mol}\cdot\text{K)}$ $n=\frac{101325\text{ Pa}\times0.500\times 10^{-3}\text{ m}^3}{8.314\text{ J/(mol}\cdot\text{K)}\times288.15\text{ K}}$ $n=\frac{50.6625\text{ J}}{2396.77\text{ J/mol}}\approx2.04\times 10^{-2}\text{ mol}$