A gas occupies 560.0 mL at 285 K. To what temperature must the gas be lowered if it is to occupy 250.0 mL? Assume that the pressure remains constant.

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To solve this problem, we can use the relationship between volume and temperature known as Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its temperature, as long as the pressure and the amount of gas are kept constant.

We can express Charles's Law mathematically as:
V1 / T1 = V2 / T2

where:
V1 = initial volume
T1 = initial temperature
V2 = final volume
T2 = final temperature

In this case, we know:
V1 = 560.0 mL
T1 = 285 K
V2 = 250.0 mL

We need to find T2, the final temperature.

Using the formula, we can rearrange it to solve for T2:
T2 = (V2 * T1) / V1

Substituting the given values, we have:
T2 = (250.0 mL * 285 K) / 560.0 mL

Calculating this expression, we find:
T2 ≈ 127.80 K

So, the gas must be lowered to approximately 127.80 K in order to occupy a volume of 250.0 mL, assuming the pressure remains constant.

Assuming the gas is ideal, we use Charles' Law to relate the relationship between Temperature & Volume of gas:

V1/T1 = V2/T2
where:
T1 = initial temperature of gas (in K)
T2 = final temperature of gas (in K)
V1 = initial volume of gas
V2 = final volume of gas
substituting,
(560)/(285) = V2/(250)
V2 = (560*250)/285
V2 = ? (units in mL)

hope this helps~ :)