Rounding to 3 Significant Figures

Oct 13, 2025 by windailys.com 21 views

Understanding the Problem

In this problem, we are tasked with determining the number of moles of gaseous butane that occupy a volume of 0.0300 L at Standard Temperature and Pressure (STP). To solve this problem, we will use the ideal gas law, which is given by the equation:

PV = nRT

where:

P is the pressure of the gas (in Pascals)
V is the volume of the gas (in cubic meters)
n is the number of moles of the gas
R is the gas constant (in Pascals per cubic meter per mole per Kelvin)
T is the temperature of the gas (in Kelvin)

Given Values

V = 0.0300 L = 0.0000300 m³ (converting liters to cubic meters)
T = 273.15 K (the temperature at STP)
R = 8.3145 J/mol·K (the gas constant)

Solving for n

We can rearrange the ideal gas law to solve for n:

n = PV / RT

Plugging in the given values, we get:

n = (101325 Pa × 0.0000300 m³) / (8.3145 J/mol·K × 273.15 K)

n ≈ 1.21 × 10^(-5) mol

Rounding to 3 Significant Figures

Rounding the result to 3 significant figures, we get:

n ≈ 1.21 × 10^(-5) mol

Therefore, the number of moles of gaseous butane that occupy 0.0300 L at STP is approximately 1.21 × 10^(-5) mol.

Conclusion

In this problem, we used the ideal gas law to determine the number of moles of gaseous butane that occupy a volume of 0.0300 L at STP. We found that the number of moles is approximately 1.21 × 10^(-5) mol. This result demonstrates the importance of understanding the ideal gas law and its application in solving problems related to gas behavior.

Part 2: Determining the Number of Moles of Gaseous Butane at a Different Temperature

In the next part of this problem, we will determine the number of moles of gaseous butane that occupy a volume of 0.0300 L at a different temperature. We will use the ideal gas law to solve for n and compare the result to the value obtained at STP.

Determining the Number of Moles of Gaseous Butane at a Different Temperature

Understanding the Problem

In this problem, we are tasked with determining the number of moles of gaseous butane that occupy a volume of 0.0300 L at a different temperature. To solve this problem, we will use the ideal gas law, which is given by the equation:

PV = nRT

where:

P is the pressure of the gas (in Pascals)
V is the volume of the gas (in cubic meters)
n is the number of moles of the gas
R is the gas constant (in Pascals per cubic meter per mole per Kelvin)
T is the temperature of the gas (in Kelvin)

Given Values

V = 0.0300 L = 0.0000300 m³ (converting liters to cubic meters)
T = 298.15 K (the temperature at which we want to determine the number of moles)
R = 8.3145 J/mol·K (the gas constant)

Solving for n

We can rearrange the ideal gas law to solve for n:

n = PV / RT

Plugging in the given values, we get:

n = (101325 Pa × 0.0000300 m³) / (8.3145 J/mol·K × 298.15 K)

n ≈ 1.23 × 10^(-5) mol

Rounding to 3 Significant Figures

Rounding the result to 3 significant figures, we get:

n ≈ 1.23 × 10^(-5) mol

Therefore, the number of moles of gaseous butane that occupy 0.0300 L at a temperature of 298.15 K is approximately 1.23 × 10^(-5) mol.

Conclusion

In this problem, we used the ideal gas law to determine the number of moles of gaseous butane that occupy a volume of 0.0300 L at a different temperature. We found that the number of moles is approximately 1.23 × 10^(-5) mol. This result demonstrates the importance of understanding the ideal gas law and its application in solving problems related to gas behavior.

Comparison of Results

In the previous part of this problem, we determined the number of moles of gaseous butane that occupy 0.0300 L at STP. We found that the number of moles is approximately 1.21 × 10^(-5) mol. In this part of the problem, we determined the number of moles of gaseous butane that occupy 0.0300 L at a temperature of 298.15 K. We found that the number of moles is approximately 1.23 × 10^(-5) mol. The results demonstrate that the number of moles of gaseous butane increases as the temperature increases, which is consistent with the ideal gas law.

Conclusion

Q: What is the ideal gas law?

A: The ideal gas law is a fundamental equation in chemistry that describes the behavior of ideal gases. It is given by the equation:

PV = nRT

where:

P is the pressure of the gas (in Pascals)
V is the volume of the gas (in cubic meters)
n is the number of moles of the gas
R is the gas constant (in Pascals per cubic meter per mole per Kelvin)
T is the temperature of the gas (in Kelvin)

Q: What is the significance of the ideal gas law?

A: The ideal gas law is a fundamental equation in chemistry that describes the behavior of ideal gases. It is used to calculate the number of moles of a gas, the pressure of a gas, the volume of a gas, and the temperature of a gas.

Q: How do I use the ideal gas law to determine the number of moles of a gas?

A: To use the ideal gas law to determine the number of moles of a gas, you need to know the pressure, volume, and temperature of the gas. You can then plug these values into the ideal gas law equation:

n = PV / RT

where:

n is the number of moles of the gas
P is the pressure of the gas (in Pascals)
V is the volume of the gas (in cubic meters)
R is the gas constant (in Pascals per cubic meter per mole per Kelvin)
T is the temperature of the gas (in Kelvin)

Q: What is the difference between the ideal gas law and the real gas law?

A: The ideal gas law is an equation that describes the behavior of ideal gases, which are gases that obey the ideal gas law. The real gas law, on the other hand, is an equation that describes the behavior of real gases, which do not obey the ideal gas law. Real gases are gases that have a non-zero volume, a non-zero pressure, and a non-zero temperature.

Q: How do I determine the number of moles of a gas at a different temperature?

A: To determine the number of moles of a gas at a different temperature, you need to know the pressure, volume, and temperature of the gas. You can then plug these values into the ideal gas law equation:

n = PV / RT

where:

n is the number of moles of the gas
P is the pressure of the gas (in Pascals)
V is the volume of the gas (in cubic meters)
R is the gas constant (in Pascals per cubic meter per mole per Kelvin)
T is the temperature of the gas (in Kelvin)

Q: What is the significance of the gas constant (R)?

A: The gas constant (R) is a fundamental constant in chemistry that describes the behavior of ideal gases. It is used in the ideal gas law equation to calculate the number of moles of a gas.

Q: How do I convert the number of moles of a gas from one unit to another?

A: To convert the number of moles of a gas from one unit to another, you need to know the conversion factor between the two units. For example, to convert the number of moles of a gas from moles to grams, you need to know the molar mass of the gas.

Conclusion

In this article, we have answered some frequently asked questions about determining the number of moles of gaseous butane. We have discussed the ideal gas law, the significance of the ideal gas law, and how to use the ideal gas law to determine the number of moles of a gas. We have also discussed the difference between the ideal gas law and the real gas law, and how to determine the number of moles of a gas at a different temperature.