How to Calculate Temperature Using Ideal Gas Law
What is the ideal gas law?
The ideal gas law is a fundamental principle in physics and chemistry that describes the behavior of a hypothetical ideal gas. The ideal gas law is expressed mathematically as:
PV = nRT
The ideal gas law describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. An ideal gas is a theoretical gas composed of a large number of randomly moving particles that do not interact with one another, except through perfectly elastic collisions. In reality, no gas behaves exactly like an ideal gas, but many gases behave approximately like an ideal gas under certain conditions.
What is temperature?
We can use the ideal gas law, which states:
PV = nRT
where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in K)
First, we need to convert the given volume to liters (since the unit of R is in L).
75.71 L = 75.71 L
Next, we can substitute the given values into the ideal gas law and solve for T:
2.68 atm x 75.71 L = 3.50 mol x 0.0821 L·atm/(mol·K) x T
202.6328 L·atm = 0.28735 mol·K·T
T = (202.6328 L·atm) / (0.28735 mol·K) = 705.6 K
Finally, we can convert the temperature from Kelvin to Celsius by subtracting 273.15:
T = 705.6 K - 273.15 = 432.45 °C
Therefore, the temperature of the sample of gas is 432.45 °C.
The ideal gas law is a powerful tool in the understanding of the behavior of gases. By using this law, we can calculate various properties of gases, such as temperature, pressure, volume, and number of moles. In this case, we utilized the ideal gas law to determine the temperature of a sample of gas given its pressure, volume, and number of moles.
Temperature is a measure of the average kinetic energy of the particles in a substance. In the context of gases, temperature is directly proportional to the average kinetic energy of gas particles. Therefore, by knowing the pressure, volume, and number of moles of a gas sample, we can use the ideal gas law to calculate the temperature of the gas.
In the calculation provided, we first converted the volume to liters and then substituted the given values into the ideal gas law equation. By solving for temperature, we found that the temperature of the gas sample is 432.45 °C. This process showcases how the ideal gas law can be applied to real-world scenarios to determine important properties of gases.