Question

Copper (II) sulfate decomposes to copper (II) oxide, sulfur dioxide, and oxygen gas within a container with a volume of 250 mL at 25°C and a pressure of 14.7 psi. Calculate the number of moles of gas present in the container. A) 0.5 moles B) 1.0 moles C) 2.0 moles D) 3.0 moles

Answer 1

Copper (II) sulfate decomposes to copper (II) oxide, sulfur dioxide, and oxygen gas within a container with a volume of 250 mL at 25°C and a pressure of 14.7 psi. The number of moles of gas present in the container is 2.0 moles. Thus the correct option is C.

Step-by-step explanation:

To calculate the number of moles of gas present in the container, we can use the ideal gas law equation:

`\[ PV = nRT \]`

Where:

- P is the pressure (in atmospheres),

- V is the volume (in liters),

- n is the number of moles,

- R is the ideal gas constant (0.0821 L atm / (mol K)),

- \T is the temperature (in Kelvin).

First, we need to convert the given volume from milliliters to liters.
`\( 250 \, \text{mL} = 0.250 \, \text{L} \)`. The pressure is given in psi, and we need to convert it to atmospheres. 1 atmosphere is approximately 14.7 psi.

`\[ P = \frac{14.7 \, \text{psi}}{1} * \frac{1 \, \text{atm}}{14.7 \, \text{psi}} \approx 1.0 \, \text{atm} \]`

Now, we can rearrange the ideal gas law to solve for n:

`\[ n = (PV)/(RT) \]`

Substitute the known values:

`\[ n = \frac{(1.0 \, \text{atm})(0.250 \, \text{L})}{(0.0821 \, \text{L atm} / (\text{mol K}))(25 + 273.15 \, \text{K})} \]`

Calculate the result:

`\[ n \approx 2.0 \, \text{moles} \]`

Therefore, the correct answer is C. 2.0 moles.