if 0.75 mole of helium gas occupies a volume of 1.5. what volume will 1.2 mole helium occupy at the same teperature and pressure?
1.5 what?
You can work this a couple of ways.
Use PV = nRT and solve for P and plug this back into PV = nRT with n = 1.2, P from above and all others being the same.
A second way is to use ratio/proportion.
(v1/n1) = (v2/n2)
A third way is to use PV = nRT but modify that so that V = nRT/P. Since R,T, & P are constants we can write that as V = nk. Plug in 1.5 and n and solve for k, then redo V = nK and plug in the k you found and the new n and solve for the new v.
Finally, since volume is proportional to mols, it is just 1.5 x 1.2/0.75 = ?
Four ways, take your pick.
To solve this problem, we'll use the mole-to-volume relationship provided by Avogadro's law.
Avogadro's law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This means that the ratio of the number of moles of two different gases is equal to the ratio of their volumes.
In this case, we have the following information:
- 0.75 moles of helium gas occupies a volume of 1.5.
- We need to find the volume of 1.2 moles of helium at the same temperature and pressure.
Now, let's set up the ratio and solve for the unknown volume.
Ratio of moles: (0.75 moles)/(1.2 moles) = (unknown volume)/(1.5 volume)
Now, let's solve for the unknown volume:
(0.75 moles)/(1.2 moles) = (unknown volume)/(1.5 volume)
Cross-multiplying:
0.75 moles * 1.5 volume = 1.2 moles * (unknown volume)
1.125 = 1.2 * (unknown volume)
Dividing both sides by 1.2:
(1.125) / (1.2) = (unknown volume)
0.9375 = (unknown volume)
Therefore, 1.2 moles of helium gas will occupy a volume of approximately 0.9375 at the same temperature and pressure.
To solve this problem, we can use the ideal gas law, which states that the product of the pressure (P), volume (V), and number of moles (n) of a gas is proportional to the temperature (T) in Kelvin.
The formula for the ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, we are given that the number of moles of helium gas is 0.75 and the volume is 1.5. Let's assume the pressure and temperature remain constant.
Now, we need to find the volume when the number of moles is 1.2. We can rearrange the ideal gas law equation to solve for V:
V = (n1 * V1) / n2
Where V is the volume, n1 is the initial number of moles, V1 is the initial volume, and n2 is the final number of moles.
Plugging in the values:
V = (0.75 * 1.5) / 1.2
V = 0.9375
Therefore, 1.2 moles of helium gas will occupy a volume of 0.9375 under the same temperature and pressure conditions.