An ideal gas is contained in a cylinder with a volume of 5.0 102 mL at a temperature of 30.°C and a pressure of 710. torr. The gas is then compressed to a volume of 38 mL, and the temperature is raised to 827°C. What is the new pressure of the gas?

torr

I held the f5 key so the views went super high up lol

I hope I didn't cause any issues by doing that, sorry

Use PV = nRT

i don't know how to use that, can you please show me?

I'm sorry. You should use (p1v1/t1) = (p1v2/t2)

v1 = 500 mL
t1 = 30 + 273 = ?K
p1 = 710 torr
v2 = 38 mL
t2 = 826 + 273 = ?K
p2 = unknown

3465

To find the new pressure of the gas, we can use the combined gas law, which states:

(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)

Where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature
P₂ = final pressure (what we're trying to find)
V₂ = final volume
T₂ = final temperature

Given:
P₁ = 710 torr
V₁ = 5.0 * 10² mL = 500 mL
T₁ = 30°C = 30 + 273.15 K (convert to Kelvin)

V₂ = 38 mL
T₂ = 827°C = 827 + 273.15 K (convert to Kelvin)

Plug in the given values and solve for P₂:

(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂

(710 torr * 500 mL) / (30 + 273.15 K) = (P₂ * 38 mL) / (827 + 273.15 K)

Simplifying the equation:

(710 torr * 500 mL * (827 + 273.15 K)) = (P₂ * 38 mL * (30 + 273.15 K))

Now, solve for P₂:

P₂ = [(710 torr * 500 mL * (827 + 273.15 K)) / (38 mL * (30 + 273.15 K))]

Calculating the value of P₂ using the equation above will give you the new pressure of the gas in torr.