Question

question 1
1 pts
how many moles of methane occupy a volume of 2.25 l at 0.0 °c and 1.00 atm? (r = 0.0821 atm·l/mol·k)
50.4 mol
0.922 mol
0.184 mol
0.100 mol
25.2 mol

Explanation:

Step1: Recall Ideal Gas Law

The Ideal Gas Law is \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is gas constant, and \( T \) is temperature in Kelvin.

Step2: Convert Temperature to Kelvin

\( T = 0.0^\circ\text{C} + 273.15 = 273.15\,\text{K} \)

Step3: Rearrange Ideal Gas Law for \( n \)

\( n=\frac{PV}{RT} \)

Step4: Substitute Values

\( P = 1.00\,\text{atm} \), \( V = 2.25\,\text{L} \), \( R = 0.0821\,\text{atm·L/mol·K} \), \( T = 273.15\,\text{K} \)
\( n=\frac{(1.00\,\text{atm})(2.25\,\text{L})}{(0.0821\,\text{atm·L/mol·K})(273.15\,\text{K})} \)
Calculate numerator: \( (1.00)(2.25)=2.25 \)
Calculate denominator: \( (0.0821)(273.15)\approx22.42 \)
\( n=\frac{2.25}{22.42}\approx0.100\,\text{mol} \)

Answer:

0.100 mol