A sample of neon gas used in a neon sign occupies a volume of 3.90 L at a pressure of 580 torr.
Calculate the volume of the gas if the pressure in the glass tube of the sign is 783 torr.
P1V1 = P2V2
To calculate the volume of the gas, we can use the combined gas law, which relates the initial and final states of a gas sample. The combined gas law formula is as follows:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 and P2 are the initial and final pressures of the gas,
V1 and V2 are the initial and final volumes of the gas,
T1 and T2 are the initial and final temperatures of the gas.
In this case, we need to find the final volume V2, given that the initial volume V1 is 3.90 L, the initial pressure P1 is 580 torr, and the final pressure P2 is 783 torr.
Since we have no information about the temperature, we can assume it remains constant throughout the process. Therefore, we can cancel out the temperature terms in the equation:
(P1 * V1) / T1 = (P2 * V2) / T2
(P1 * V1) = (P2 * V2)
Now we can plug in the values we know:
(580 torr * 3.90 L) = (783 torr * V2)
To find V2, we can rearrange the equation and solve for V2:
V2 = (580 torr * 3.90 L) / 783 torr
V2 = 2.885 L
Therefore, the volume of the neon gas at a pressure of 783 torr is approximately 2.885 L.