A sample of nitrogen has a volume of 50.0L at a pressure of 760mmHg. What is the volume of the gas at each of the following pressures if there is no change in temperature?

A. 1500mmHg B. 2.0atm C. 0.500atm

At constant temperature,

P * V = constant

Use that fact to solve for V in each case. You can leave the pressures in units of mm of mercury (Hg)

For example, at P = 1500 mm Hg,
P = 50*760/1500 = ___ mm Hg

To solve this problem, we can use Boyle's Law, which states that at constant temperature, the pressure and volume of a gas are inversely proportional.

Boyle's Law equation: P1 * V1 = P2 * V2

Given:
Initial volume (V1) = 50.0 L
Initial pressure (P1) = 760 mmHg

A. To find the volume at 1500 mmHg:
P2 = 1500 mmHg
Using the Boyle's Law equation:
P1 * V1 = P2 * V2
V2 = (P1 * V1) / P2

Plugging in the values:
V2 = (760 mmHg * 50.0 L) / 1500 mmHg
V2 = 25.3 L

Therefore, the volume of the gas at a pressure of 1500 mmHg is 25.3 L.

B. To find the volume at 2.0 atm:
P2 = 2.0 atm
Since the pressure is given in atm, we need to convert the initial pressure from mmHg to atm.
1 atm = 760 mmHg

Converting the initial pressure:
Initial pressure (P1) = 760 mmHg / 760 mmHg/atm = 1 atm

Using the Boyle's Law equation:
P1 * V1 = P2 * V2
V2 = (P1 * V1) / P2

Plugging in the values:
V2 = (1 atm * 50.0 L) / 2.0 atm
V2 = 25.0 L

Therefore, the volume of the gas at a pressure of 2.0 atm is 25.0 L.

C. To find the volume at 0.500 atm:
P2 = 0.500 atm
Using the Boyle's Law equation:
P1 * V1 = P2 * V2
V2 = (P1 * V1) / P2

Plugging in the values:
V2 = (1 atm * 50.0 L) / 0.500 atm
V2 = 100 L

Therefore, the volume of the gas at a pressure of 0.500 atm is 100 L.

To solve this problem, we can use Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure, as long as the temperature remains constant.

Boyle's Law equation can be written as:
P1 * V1 = P2 * V2

Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas

We are given:
P1 = 760 mmHg
V1 = 50.0 L

Now let's solve for each case:

A. When the pressure is 1500 mmHg:
P2 = 1500 mmHg

Using the formula, we can solve for V2:
P1 * V1 = P2 * V2
(760 mmHg) * (50.0 L) = (1500 mmHg) * V2

Now we can plug in the values and solve for V2:
(760 mmHg) * (50.0 L) = (1500 mmHg) * V2
V2 = (760 mmHg * 50.0 L) / (1500 mmHg)
V2 = 25.33 L

So, the volume of the gas at 1500 mmHg would be 25.33 L.

B. When the pressure is 2.0 atm:
P2 = 2.0 atm

Using the Boyle's Law equation:
P1 * V1 = P2 * V2
(760 mmHg) * (50.0 L) = (2.0 atm) * V2

To use the same units, we need to convert atm to mmHg:
1 atm = 760 mmHg

Now let's convert the pressure:
P2 = (2.0 atm) * (760 mmHg/atm)
P2 = 1520 mmHg

Using the formula, we can solve for V2:
(760 mmHg) * (50.0 L) = (1520 mmHg) * V2

Now we can plug in the values and solve for V2:
(760 mmHg) * (50.0 L) = (1520 mmHg) * V2
V2 = (760 mmHg * 50.0 L) / (1520 mmHg)
V2 = 25.00 L

So, the volume of the gas at 2.0 atm would be 25.00 L.

C. When the pressure is 0.500 atm:
P2 = 0.500 atm

Using the Boyle's Law equation:
P1 * V1 = P2 * V2
(760 mmHg) * (50.0 L) = (0.500 atm) * V2

To use the same units, we need to convert atm to mmHg:
1 atm = 760 mmHg

Now let's convert the pressure:
P2 = (0.500 atm) * (760 mmHg/atm)
P2 = 380 mmHg

Using the formula, we can solve for V2:
(760 mmHg) * (50.0 L) = (380 mmHg) * V2

Now we can plug in the values and solve for V2:
(760 mmHg) * (50.0 L) = (380 mmHg) * V2
V2 = (760 mmHg * 50.0 L) / (380 mmHg)
V2 = 100.00 L

So, the volume of the gas at 0.500 atm would be 100.00 L.