Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
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]
[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]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.