Answered

IDNLearn.com connects you with a community of knowledgeable individuals ready to help. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.

What is the volume of 0.200 mol of an ideal gas at [tex]200 \, \text{kPa}[/tex] and [tex]400 \, \text{K}[/tex]?

Use [tex]PV = nRT[/tex] and [tex]R = 8.314 \frac{L \cdot kPa}{mol \cdot K}[/tex].

A. [tex]0.83 \, L[/tex]
B. [tex]3.33 \, L[/tex]
C. [tex]5.60 \, L[/tex]
D. [tex]20.8 \, L[/tex]

Sagot :

GinnyAnsweridn
To solve for the volume [tex]\( V \)[/tex] of an ideal gas using the ideal gas law [tex]\( PV = nRT \)[/tex], we need to rearrange the equation to solve for [tex]\( V \)[/tex]:
[tex]\[ V = \frac{nRT}{P} \][/tex]

Let's plug in the given values:
- [tex]\( P \)[/tex] (Pressure) = 200 kPa
- [tex]\( n \)[/tex] (Number of moles) = 0.200 mol
- [tex]\( R \)[/tex] (Ideal gas constant) = 8.314 \frac{L \cdot kPa}{mol \cdot K}
- [tex]\( T \)[/tex] (Temperature) = 400 K

Now, substitute these values into the equation:
[tex]\[ V = \frac{0.200 \, \text{mol} \times 8.314 \, \frac{L \cdot kPa}{mol \cdot K} \times 400 \, K}{200 \, kPa} \][/tex]

Perform the multiplication and division:
[tex]\[ V = \frac{0.200 \times 8.314 \times 400}{200} \][/tex]

[tex]\[ V = \frac{665.12}{200} \][/tex]

[tex]\[ V = 3.3256 \, L \][/tex]

Therefore, the volume of the gas is approximately:
[tex]\[ V = 3.33 \, L \][/tex]

So, the correct answer is:
[tex]\[ \boxed{3.33 \, L} \][/tex]
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.