When the pressure exerted on 1.0L of an ideal gas is quadrupled, and the kelvin temperature is tripled,what does the volume become?

use combined gas laws

Another way to look at this is ... changes in volume are pressure and temperature sensitive...

=> Increasing Pressure => Decreasing Volume and Decreasing Pressure Increasing Volume.

=> Increasing Temperature => Increasing Volume and Decreasing Temperature => Decreasing Volume.

So from your problem, if pressure is increased Volume MUST 'Decrease' and if temperature is 'Increased' the volume MUST 'Increase'.

To set this up ...
V(final) = [V(initial)](Pressure Effects)(Temperature Effects)

V(initial)=V(1) --- V(final)=V(2)
P(initial)=P(1) --- P(final)=P(2)=4[P(1)]
T(initial)=T(1) --- T(final)=T(2)=3[T(1)]

V(final) = V(1)[Ratio of P(1):P(2) that will cause V(1) to 'Decrease'][Ratio of T(1):T(2) that will cause V(1) to 'Increase']

V(final) = V(1)[(P(1)/P(2)][T(2)/T(1)] = V(1)[P(1)/4P(1)][3T(1)/T(1)] = V(1)(1/4)(3/1) = (3/4)V(1) ... The final volume will be smaller than initial volume because the 'Pressure Effect' is greater than the 'Temperature Effect'.

To determine the new volume of the gas when the pressure and temperature are changed, we can use the combined gas law. The combined gas law describes the relationship between pressure, volume, and temperature of a gas.

The combined gas law equation is:

(P1 × V1) / T1 = (P2 × V2) / T2

Where:
P1 is the initial pressure of the gas
V1 is the initial volume of the gas
T1 is the initial temperature of the gas
P2 is the final pressure of the gas
V2 is the final volume of the gas (what we want to find)
T2 is the final temperature of the gas

Let's plug in the given values:

P1 = Initial pressure = 1.0 atm (since we are using ideal gas units)
V1 = Initial volume = 1.0 L
T1 = Initial temperature
P2 = Final pressure = Quadrupled initial pressure = 4×P1 = 4×1.0 atm = 4.0 atm
V2 = Final volume (what we want to find)
T2 = Final temperature = Tripled initial temperature = 3×T1

Now, we'll solve the equation to find V2:

(P1 × V1) / T1 = (P2 × V2) / T2

(1.0 atm × 1.0 L) / T1 = (4.0 atm × V2) / (3 × T1)

Simplifying the equation:

V2 = (1.0 atm × 1.0 L × 3 × T1) / (4.0 atm × 1.0)

V2 = (3 × T1) / 4

Since the initial volume, V1, is given as 1.0 L, the answer so far will be relative to the initial volume (V1). So, by plugging V1 into the equation, we get:

V2 = (3 × T1) / 4 × V1

V2 = (3 × T1) / 4 × 1.0 L

Now, to determine the final volume, we need to know the initial temperature, T1. If you provide the initial temperature value, I can help you find the final volume.