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- 2 weeks ago
P * V = n * R * T

That's the ideal gas equation. Since we're treating n and R as constants, we can rewrite this:

P * V / T = n * R

P * V / T = k

P[1] * V[1] / T[1] = k

P[2] * V[2] / T[2] = k

therefore

P[1] * V[1] / T[1] = P[2] * V[2] / T[2]

This is the combined gas law.

P[1] = 3 * 10^4 atm

P[2] = 3 * 10^(-3) atm

V[1] = 6 * 10^(-4) cm^3

V[2] = ?

T[1] = 90 Kelvins

T[2] = 3 Kelvins

If we make sure that the unknown volume is in cubic centimeters, then we can forego the units, for the sake of simplicity.

3 * 10^4 * 6 * 10^(-4) / 90 = 3 * 10^(-3) * V / 3

(18/90) * 10^(4 - 4) = (3/3) * 10^(-3) * V

(1/5) * 10^(0) = 1 * 10^(-3) = V

(1/5) * 10^3 = V

1000/5 = V

200 = V

200 cubic cm, or in scientific notation 2 * 10^(2) cm^3

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