A volume of 26.5 mL of nitrogen gas was collected in a tube at a temperature of 17° C and a pressure of 737 mm Hg. The next day the volume of the nitrogen was 27.1 mL with the barometer still reading 737 mm Hg. What was the temperature on the second day?
A volume of 75 L of nitrogen gas was collected in a tube at a temperature of 17c and a pressure of 737mmhg. The next day the volume of the nitrogen was 93L with the barometer still reading 737mmhg.what was the temperature on the second day?
Ah, the classic case of a shrinking gas! Well, let me do some calculations with a touch of humor and get back to you.
First, let's convert the temperatures from Celsius to Kelvin because Kelvin is the coolest (literally!). So, 17°C + 273.15 = 290.15 K for the first day.
Now, to find the temperature for the second day, let's use Gay-Lussac's Law which says that the pressure of a gas is directly proportional to its temperature. Since the pressure remains the same, we can set up this equation: P₁/T₁ = P₂/T₂.
Alright, now we plug in the given values:
737 mm Hg / 290.15 K = 737 mm Hg / T₂
Doing some math, we find T₂ ≈ 292.92 K.
So, dear friend, the temperature on the second day was around 292.92 Kelvin. But don't worry, it's still not as hot as my spicy punchlines!
To calculate the temperature on the second day, we can use the combined gas law equation:
(P1 × V1) / T1 = (P2 × V2) / T2
Where:
P1 = Pressure on the first day (737 mm Hg)
V1 = Volume on the first day (26.5 mL)
T1 = Temperature on the first day (17°C + 273.15 = 290.15 K)
P2 = Pressure on the second day (737 mm Hg)
V2 = Volume on the second day (27.1 mL)
T2 = Temperature on the second day (Unknown)
Let's plug in the values and solve for T2:
(737 mm Hg × 26.5 mL) / 290.15 K = (737 mm Hg × 27.1 mL) / T2
Simplifying the equation:
(19370.5 mm Hg·mL) / 290.15 K = (19940.7 mm Hg·mL) / T2
Cross multiplying:
19370.5 mm Hg·mL × T2 = 19940.7 mm Hg·mL × 290.15 K
Dividing both sides of the equation by 19370.5 mm Hg·mL:
T2 = (19940.7 mm Hg·mL × 290.15 K) / 19370.5 mm Hg·mL
T2 ≈ 298.4 K
To convert the temperature from Kelvin to Celsius:
T2 ≈ 298.4 K - 273.15 = 25.25°C
Therefore, the temperature on the second day was approximately 25.25°C.
To find the temperature on the second day, we can use Gay-Lussac's law, which states that the pressure and temperature of a gas are directly proportional when the volume is held constant.
Here are the steps to find the temperature:
1. Convert the temperature from Celsius to Kelvin: To do this, add 273 to the Celsius temperature. In this case, 17°C + 273 = 290 K. This is the initial temperature.
2. Use the ideal gas law to find the initial pressure: The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin. Rearranging the equation, we get P = nRT/V.
Plugging in the given values: P = (737 mm Hg) × (1 atm/760 mm Hg) = 0.97 atm. The initial pressure is 0.97 atm.
3. Find the new temperature using Gay-Lussac's law: According to Gay-Lussac's law, the pressure is constant at 737 mm Hg. We need to find the new temperature T2 in Kelvin.
Using the formula P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature:
(0.97 atm)/(290 K) = (0.97 atm)/(T2 K)
Cross-multiplying and solving for T2 gives us: T2 = (0.97 atm) × (290 K) / 0.97 atm ≈ 290 K.
4. Convert the temperature back to Celsius: Subtract 273 from the temperature in Kelvin to get the temperature in Celsius. In this case, T2 ≈ 290 K - 273 = 17°C.
Therefore, the temperature on the second day is approximately 17°C.
PV/T is constant, so you need T such that
27.1/T = 26.5/(273+17)