1.0 dm3 of an ideal gas at 100 kPa and 25 °C is heated to 50 °C at constant pressure. What is the new volume in dm3?

To solve this problem, we can use the ideal gas law, which states that the pressure of a gas times its volume is proportional to the number of gas molecules and the temperature of the gas. This can be written as:

PV = nRT

where: P is the pressure, V is the volume, n is the number of molecules, R is the gas constant, and T is the temperature.

In this problem, the pressure P is constant, the number of molecules n is constant (because the amount of gas doesn't change), and R is always constant. So we can simplify the equation to:

V1/T1 = V2/T2

where: V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.

We are given that V1 = 1.0 dm3, T1 = 25 °C, and T2 = 50 °C. We want to find V2.

First, we need to convert the temperatures from Celsius to Kelvin, because the ideal gas law requires temperatures to be in Kelvin. The conversion is:

K = °C + 273.15

So T1 = 25 °C + 273.15 = 298.15 K and T2 = 50 °C + 273.15 = 323.15 K.

Now we can plug these values into the equation:

1.0 dm3 / 298.15 K = V2 / 323.15 K

Solving for V2 gives:

V2 = 1.0 dm3 * 323.15 K / 298.15 K = 1.084 dm3

So the new volume of the gas is approximately 1.084 dm3.