The volume of a sample of oxygen is 200.0 mL when the pressure is 3.000 atm and the temperature is 37.0 oC. What is the new temperature if the volume increases to 400.0 mL and the pressure decreases to 2.000 atm?

To solve this problem, we can use the combined gas law equation:

(P1 x V1)/(T1) = (P2 x V2)/(T2)

Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure
V2= Final volume
T2 = Final temperature

We are given:
P1 = 3.000 atm
V1 = 200.0 mL
T1 = 37.0 oC
P2 = 2.000 atm
V2 = 400.0 mL

Let's plug the given values into the equation and solve for T2:

(3.000 atm x 200.0 mL)/(37.0 oC) = (2.000 atm x 400.0 mL)/(T2)

Now, we can cross multiply:

(3.000 atm x 200.0 mL) x (T2) = (2.000 atm x 400.0 mL) x (37.0 oC)

Next, we simplify the equation:

600.0 atm.mL x (T2) = 800.0 atm.mL x (37.0 oC)

To isolate T2, we divide both sides by 600.0 atm.mL:

(T2) = (800.0 atm.mL x 37.0 oC)/600.0 atm.mL

Now, we can calculate:

T2 = 59200.0 atm.mL.oC/600.0 atm.mL
T2 = 98.67 oC

Therefore, the new temperature is 98.67 oC.

To find the new temperature, we can use the combined gas law, which relates the initial and final states of a gas sample. The combined gas law equation is:

(P1 × V1) / (T1) = (P2 × V2) / (T2)

where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.

We have the initial values:
P1 = 3.000 atm
V1 = 200.0 mL
T1 = 37.0 °C

We need to find the final temperature T2, given the final values:
P2 = 2.000 atm
V2 = 400.0 mL

First, let's convert the temperatures from Celsius to Kelvin since temperature must be expressed in Kelvin in gas law equations. To convert from Celsius to Kelvin, we use the equation:

T(K) = T(°C) + 273.15

So, we have:
T1 = 37.0 °C + 273.15 = 310.15 K

Now we can substitute the values into the combined gas law equation:

(3.000 atm × 200.0 mL) / (310.15 K) = (2.000 atm × 400.0 mL) / (T2)

We can rearrange the equation to solve for T2:

T2 = (2.000 atm × 400.0 mL) / [(3.000 atm × 200.0 mL) / (310.15 K)]

T2 = (2.000 atm × 400.0 mL × 310.15 K) / (3.000 atm × 200.0 mL)

T2 = (2.000 × 400.0 × 310.15) / (3.000 × 200.0)

Now we can calculate the value of T2:

T2 = 165.43 K

Therefore, the new temperature is 165.43 K.

140.3

Use PV = nRT. Remember to convert T to kelvin. The answer you want will come out in kelvin so remember to convert back to C if you want the anwer in degrees C. Also remember to convert mL to L. L is the unit for V. Post your work if you get stuck.