A gas occupies 10 liters at standard conditions. What volume will it occupy at 20 degrees celsius and 700 torr?
Use PV = nRT.
Convert torr to atm.
Convert C to Kelvin
To solve this problem, you can use the combined gas law equation, which relates the initial and final conditions of a gas. The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2),
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin.
First, let's convert the initial temperature from degrees Celsius to Kelvin by adding 273.15:
T1 = 20°C + 273.15 = 293.15 K.
Next, we need to convert the initial volume from liters to a standard unit, which is usually expressed as cubic meters (m³). Since 1 cubic meter is equal to 1000 liters, we can convert 10 liters to cubic meters:
V1 = 10 L * (1 m³ / 1000 L) = 0.01 m³.
Now, we can substitute the given values into the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2,
where P1 is the standard pressure at standard conditions (1 atm or 760 torr), V1 is 0.01 m³, T1 is 293.15 K, P2 is 700 torr, and T2 is the final temperature in Kelvin.
Let's solve for V2:
(1 atm * 0.01 m³) / 293.15 K = (700 torr * V2) / T2.
Since we know that 1 atm is equivalent to 760 torr and we want to find V2, we can rearrange the equation to solve for V2:
V2 = (1 atm * 0.01 m³ * T2) / (760 torr).
Since T2 is 20°C + 273.15 = 293.15 K, we can substitute this value into the equation:
V2 = (1 atm * 0.01 m³ * 293.15 K) / (760 torr).
Simplifying the equation gives us the final volume:
V2 = (0.00013086519 m³ * K) / (torr).
Now, we just need to convert the volume from cubic meters to liters by multiplying by 1000:
V2 = 0.13086519 L.
Therefore, the gas will occupy approximately 0.13 liters at 20 degrees Celsius and 700 torr.