Please help!
How many moles of hydrogen are needed to triple the volume occupied by 0.25 mol of hydrogen, assuming no changes in pressure or temperature
You can figure this yourself two ways.
1. intuitive. You figure 3 times 0.25 should occupy 3 times as much.
2. with math. PV = nRT and solve for
V = nRT/P. If R, T, and P are constant, then
V = n*some k.
So if we want V to be 3x, we need to have 3n*k.
To calculate the number of moles of hydrogen needed to triple the volume occupied by 0.25 mol of hydrogen, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the pressure and temperature remain constant, we can rewrite the equation as:
V = nR (constant)
To triple the volume, we need 3 times the initial volume. Therefore, the final volume is 3 times the initial volume:
V_final = 3V_initial
Since the number of moles (n) is also proportional to volume (V), we can write:
n_final / n_initial = V_final / V_initial
Plugging in the values, we get:
n_final / 0.25 mol = 3 V_initial / V_initial
Simplifying:
n_final / 0.25 mol = 3
To solve for n_final, multiply both sides by 0.25 mol:
n_final = 0.25 mol * 3
n_final = 0.75 mol
Therefore, you would need 0.75 moles of hydrogen to triple the volume occupied by 0.25 mol of hydrogen.
To find out how many moles of hydrogen are needed to triple the volume, we can start by using the ideal gas law equation, which states:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature
Since the question states that there are no changes in pressure or temperature, we can assume that these values are constant. Therefore, we can simplify the equation to:
V = nR
Now, let's analyze the given situation. We have 0.25 mol of hydrogen occupying a certain volume. To triple this volume, we need to find out how many moles of hydrogen are needed.
First, solve the equation for the initial volume:
V1 = n1R
Then, calculate the volume after tripling:
V2 = 3V1 = 3n1R
Now, rearrange the equation to solve for n2, the number of moles needed to triple the volume:
V2 = n2R
Divide both sides of the equation by R:
n2 = V2/R
Finally, substitute the values into the equation:
n2 = (3n1R) / R
R cancels out, and we are left with:
n2 = 3n1
So, to triple the volume, we need 3 times the initial number of moles of hydrogen.
In this case, the initial number of moles is 0.25 mol, so to triple the volume, we would need:
n2 = 3 x 0.25 mol
= 0.75 mol
Therefore, 0.75 moles of hydrogen are needed to triple the volume occupied by 0.25 mol of hydrogen.