A chemist prepares a sample of hydrogen bromide and finds that it occupies 249 mL at 60◦C and 552 Torr. What volume would it occupy at 0◦C at the same pressure? Answer in units of mL

What’s the answer

To solve this problem, we can use the Combined Gas Law equation:

(P₁ × V₁)/(T₁) = (P₂ × V₂)/(T₂)

Where:
P₁ = Initial pressure (in this case, 552 Torr)
V₁ = Initial volume (in this case, 249 mL)
T₁ = Initial temperature (in this case, 60◦C + 273.15 = 333.15 K)
P₂ = Final pressure (same as initial pressure, 552 Torr)
V₂ = Final volume (what we are trying to find)
T₂ = Final temperature (0◦C + 273.15 = 273.15 K)

We can now substitute the given values into the equation:

(552 Torr × 249 mL)/(333.15 K) = (552 Torr × V₂)/(273.15 K)

Now, we can solve for V₂:

(552 Torr × 249 mL × 273.15 K) / (333.15 K) = 552 Torr × V₂

Canceling out the units:

V₂ = (552 Torr × 249 mL × 273.15 K) / (552 Torr)
V₂ = 249 mL × 273.15 K
V₂ = 68,362.35 mL

Therefore, the sample of hydrogen bromide would occupy 68,362.35 mL at 0◦C and the same pressure.

To find the volume that the sample of hydrogen bromide would occupy at 0°C at the same pressure, we can make use of the combined gas law. The combined gas law relates the volume, temperature, and pressure of a gas.

The combined gas law equation is:

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

Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature

Given values:
P1 = 552 Torr
V1 = 249 mL
T1 = 60°C + 273.15 (converting to Kelvin, where 0°C = 273.15 K)
P2 = 552 Torr
T2 = 0°C + 273.15 (converting to Kelvin)

Now, let's plug in the values into the equation:

(552 Torr * 249 mL) / (60°C + 273.15 K) = (552 Torr * V2) / (0°C + 273.15 K)

Simplifying:

(552 Torr * 249 mL) / (333.15 K) = (552 Torr * V2) / (273.15 K)

To isolate V2, our unknown variable, we can cross-multiply and solve for V2:

(552 Torr * V2) = (552 Torr * 249 mL * 273.15 K) / (333.15 K)

Now, divide both sides of the equation by 552 Torr to solve for V2:

V2 = (249 mL * 273.15 K) / (333.15 K)

Calculating this expression gives us:

V2 = 203.96 mL

Therefore, the volume that the sample of hydrogen bromide would occupy at 0°C at the same pressure is approximately 203.96 mL.

(V1/T1) = (V2/T2)

Don't forget T must be in kelvin.