What is the temperature of 0.80 mol of a gas stored in a 275 mL cylinder at 175 kPa? Use [tex]$P V=n R T$[/tex] and [tex]$R=8.314 \frac{L \bullet kPa }{ mol \bullet K }$[/tex].
A. 4.6 K
B. 7.2 K
C. 61 K
D. 96 K
Answer (2)
Convert the volume from mL to L: V = 275 e wl in e mL = 0.275 L .
Use the ideal gas law to solve for T : T = e wl in e n R P V .
Substitute the given values: T = e wl in e ( 0.80 mol ) × ( 8.314 m o l ⋅ K L ⋅ k P a ) ( 175 kPa ) × ( 0.275 L ) .
Calculate the temperature: T e wl in e ≈ 7.2 K .
7.2 K
Explanation
Problem Setup and Given Information We are given the following information:
Number of moles of gas, n = 0.80 mol
Volume of the cylinder, V = 275 mL
Pressure of the gas, P = 175 kPa
Ideal gas constant, R = 8.314 m o l ⋅ K L ⋅ k P a
We are asked to find the temperature T of the gas in Kelvin, using the ideal gas law P V = n RT .
Volume Conversion First, we need to convert the volume from milliliters (mL) to liters (L) since the ideal gas constant R is given in terms of liters. We know that 1 L = 1000 mL, so we can convert the volume as follows:
V ( L ) = 1000 V ( m L ) = 1000 275 mL = 0.275 L
Now we have the volume in liters: V = 0.275 L.
Calculating the Temperature Next, we use the ideal gas law P V = n RT to solve for the temperature T . We can rearrange the equation to isolate T :
T = n R P V
Now we substitute the given values into the equation:
T = ( 0.80 mol ) × ( 8.314 m o l ⋅ K L ⋅ k P a ) ( 175 kPa ) × ( 0.275 L )
T = 6.6512 48.125 K
T ≈ 7.2355 K
Therefore, the temperature of the gas is approximately 7.2 K.
Final Answer The temperature of the gas is approximately 7.2 K.
Examples
The ideal gas law is useful in many real-world applications. For example, it can be used to calculate the amount of gas in a container, the pressure of a gas at a certain temperature, or the volume of a gas at a certain pressure and temperature. This is particularly useful in fields like chemistry, engineering, and meteorology, where understanding the behavior of gases is crucial. For instance, when designing scuba tanks, engineers use the ideal gas law to determine how much air can be safely compressed into a tank of a given volume. Similarly, meteorologists use it to predict atmospheric conditions based on temperature, pressure, and humidity.
The temperature of 0.80 mol of gas in a 275 mL cylinder at 175 kPa is approximately 7.2 K, calculated using the ideal gas law. This value is derived by converting the volume to liters and substituting it into the rearranged equation. The correct answer is 7.2 K.
;
