if 3.21 mol of a gas occupies 56.2 liters at 44 degrees celcius and 793 torr, 5.29 mol of this gas occupies how many liters under these conditions?
Isn't that just 56.2 L x (5.29/3.21) = ??
Check my thinking. Note the correct spelling of celsius.
Well, well, well, it seems like you're trying to gas me up with this question! Don't worry, I've got some humor that might lighten things up.
So, if we have 3.21 moles of gas taking up 56.2 liters, let's call this the "gas dance." Now, if you wanna invite 5.29 moles to this party, we need to figure out how much space it's gonna take.
First, we need to know the temperature and pressure to keep our gas in check. You mentioned it's 44 degrees Celsius and 793 torr. Let me grab my funny formulas, where temperature is measured in Kelvins and volume is measured in liters. Picture this: we're doing the cha-cha with numbers!
To convert from Celsius to Kelvin, add 273.15. So 44 degrees Celsius + 273.15 = 317.15 K. We're sizzling now!
Now, mathematically speaking, we can use the combined gas law to solve this conundrum:
(P1 × V1) ÷ (T1) = (P2 × V2) ÷ (T2)
Where:
P1 = 793 torr (pressure of the first dance)
V1 = 56.2 liters (volume of the first dance)
T1 = 317.15 K (temperature of the first dance)
P2 = What we're searching for (pressure of the second dance)
V2 = What we want to know (volume of the second dance)
T2 = 317.15 K (temperature of the second dance)
Ready? Let's apply the gas law with some clown flair. I'll do some number magic, just for you!
(793 torr × 56.2 liters) ÷ 317.15 K = (P2 × V2) ÷ 317.15 K
Now, let's solve for V2, the volume of our second dance:
(793 torr × 56.2 liters) ÷ 317.15 K = (P2 × V2)
No worries, I'm putting on my hilarious hat of calculations! Dividing both sides by P2, we get:
((793 torr × 56.2 liters) ÷ 317.15 K) ÷ P2 = V2
Now, let's plug in some numbers:
((793 torr × 56.2 liters) ÷ 317.15 K) ÷ 5.29 mol = V2
And voila! Solving that equation will give you the volume (V2) in liters for 5.29 moles of this gas, under these spicy conditions. I hope this gas dance was a breeze for you!
To find out how many liters 5.29 mol of the gas occupies under the given conditions, you can use the gas law equation:
PV = nRT
Where:
P = pressure (in this case, 793 torr)
V = volume (unknown, what we are trying to find)
n = number of moles of gas (5.29 mol)
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature in Kelvin (44 degrees Celsius + 273.15 = 317.15 K)
First, rearrange the equation to solve for V:
V = (nRT) / P
Now plug in the values:
V = (5.29 mol * 0.0821 L·atm/(K·mol) * 317.15 K) / 793 torr
Simplify the equation:
V = (137.33049 L·atm) / 793 torr
Since we want the answer in liters, convert torr to atm (1 atm = 760 torr):
V = (137.33049 L·atm) / (793 torr / 760 torr/atm)
V = (137.33049 L·atm) / (1.05 atm)
V ≈ 130.8 liters
Therefore, 5.29 mol of this gas occupies approximately 130.8 liters under the given conditions.
To determine the number of liters occupied by 5.29 mol of the gas under the given conditions, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in this case, 793 torr)
V = volume (what we want to find)
n = moles of gas (5.29 mol)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (44 degrees Celsius + 273.15 = 317.15 K)
First, we rearrange the equation to solve for V:
V = (nRT) / P
Now we can plug in the values and calculate:
V = (5.29 mol * 0.0821 L·atm/mol·K * 317.15 K) / 793 torr
We need to convert torr to atm:
1 atm = 760 torr
V = (5.29 mol * 0.0821 L·atm/mol·K * 317.15 K) / (793 torr / 760 torr/atm)
Simplifying the equation:
V = (5.29 mol * 0.0821 L·atm/mol·K * 317.15 K) / (793 torr / 760)
V ≈ 13.33 liters
Therefore, 5.29 mol of the gas would occupy approximately 13.33 liters under these conditions.