We appreciate your visit to 4 00 moles of an ideal gas occupy a volume of tex 100 0 L tex at a pressure of tex 99 1 kPa tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
- Convert the temperature from Celsius to Kelvin: $T(K) = 25.0 + 273.15 = 298.15 K$.
- Apply the ideal gas law: $R = \frac{PV}{nT}$.
- Substitute the given values: $R = \frac{(99.1 kPa)(100.0 L)}{(4.00 mol)(298.15 K)}$.
- Calculate and round the result to three significant digits: $R \approx \boxed{8.31}$.
### Explanation
1. Problem Setup and Given Data
We are given the number of moles ($n = 4.00$), volume ($V = 100.0 L$), pressure ($P = 99.1 kPa$), and temperature in Celsius ($T = 25.0^{\circ} C$) of an ideal gas. We need to find the gas constant $R$ in $\frac{L \cdot kPa}{mol \cdot K}$.
2. Convert Celsius to Kelvin
First, convert the temperature from Celsius to Kelvin: $$T(K) = T(^{\circ} C) + 273.15$$ $$T(K) = 25.0 + 273.15 = 298.15 K$$
3. Applying the Ideal Gas Law
Now, use the ideal gas law to solve for $R$: $$PV = nRT$$ $$R = \frac{PV}{nT}$$
4. Substituting Values
Substitute the given values into the equation: $$R = \frac{(99.1 kPa)(100.0 L)}{(4.00 mol)(298.15 K)}$$ $$R = \frac{9910}{1192.6} \frac{L \cdot kPa}{mol \cdot K}$$
5. Calculating R
Calculate the value of $R$: $$R = 8.309575716921014 \frac{L \cdot kPa}{mol \cdot K}$$
6. Rounding the Result
Round the result to three significant digits: $$R \approx 8.31 \frac{L \cdot kPa}{mol \cdot K}$$
7. Final Answer
The value of the gas constant $R$ is approximately 8.31.
### Examples
The ideal gas law, used to calculate the gas constant, is crucial in various real-world applications. For instance, it helps predict the behavior of gases in engines, design efficient air conditioning systems, and determine the amount of gas in scuba tanks. Understanding gas behavior is also essential in industrial processes like synthesizing ammonia or producing polymers, where precise control of temperature, pressure, and volume is necessary for optimal results. By mastering these concepts, engineers and scientists can create and improve technologies that impact our daily lives.
- Apply the ideal gas law: $R = \frac{PV}{nT}$.
- Substitute the given values: $R = \frac{(99.1 kPa)(100.0 L)}{(4.00 mol)(298.15 K)}$.
- Calculate and round the result to three significant digits: $R \approx \boxed{8.31}$.
### Explanation
1. Problem Setup and Given Data
We are given the number of moles ($n = 4.00$), volume ($V = 100.0 L$), pressure ($P = 99.1 kPa$), and temperature in Celsius ($T = 25.0^{\circ} C$) of an ideal gas. We need to find the gas constant $R$ in $\frac{L \cdot kPa}{mol \cdot K}$.
2. Convert Celsius to Kelvin
First, convert the temperature from Celsius to Kelvin: $$T(K) = T(^{\circ} C) + 273.15$$ $$T(K) = 25.0 + 273.15 = 298.15 K$$
3. Applying the Ideal Gas Law
Now, use the ideal gas law to solve for $R$: $$PV = nRT$$ $$R = \frac{PV}{nT}$$
4. Substituting Values
Substitute the given values into the equation: $$R = \frac{(99.1 kPa)(100.0 L)}{(4.00 mol)(298.15 K)}$$ $$R = \frac{9910}{1192.6} \frac{L \cdot kPa}{mol \cdot K}$$
5. Calculating R
Calculate the value of $R$: $$R = 8.309575716921014 \frac{L \cdot kPa}{mol \cdot K}$$
6. Rounding the Result
Round the result to three significant digits: $$R \approx 8.31 \frac{L \cdot kPa}{mol \cdot K}$$
7. Final Answer
The value of the gas constant $R$ is approximately 8.31.
### Examples
The ideal gas law, used to calculate the gas constant, is crucial in various real-world applications. For instance, it helps predict the behavior of gases in engines, design efficient air conditioning systems, and determine the amount of gas in scuba tanks. Understanding gas behavior is also essential in industrial processes like synthesizing ammonia or producing polymers, where precise control of temperature, pressure, and volume is necessary for optimal results. By mastering these concepts, engineers and scientists can create and improve technologies that impact our daily lives.
Thanks for taking the time to read 4 00 moles of an ideal gas occupy a volume of tex 100 0 L tex at a pressure of tex 99 1 kPa tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
