Question

how many moles of oxygen must be placed in a 3.00 liter container in order to exert a pressure of 2.00 atmospheres at 25°c?

Explanation:

Step1: Convert temperature to Kelvin

The temperature \( T = 25^{\circ}C\). To convert to Kelvin, use \( T(K)=T(^{\circ}C)+273.15\). So \(T = 25 + 273.15=298.15K\).

Step2: Apply the ideal gas law

The ideal gas law is \(PV = nRT\), where \(P = 2.00\ atm\), \(V=3.00\ L\), \(R = 0.0821\ L\cdot atm/(mol\cdot K)\). We need to solve for \(n\) (moles). Rearranging the formula gives \(n=\frac{PV}{RT}\).
Substitute the values: \(n=\frac{2.00\times3.00}{0.0821\times298.15}\).
First, calculate the numerator: \(2.00\times3.00 = 6.00\).
Then, calculate the denominator: \(0.0821\times298.15\approx24.48\).
Now, \(n=\frac{6.00}{24.48}\approx0.245\ mol\).

Answer:

0.245 moles