Anonymous asked in Science & MathematicsMathematics · 1 month ago

WHATS THE "?" idgi please explain step by step?

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1 Answer

  • 1 month ago
    Favourite answer

    Ideal gas Law's equation is:

    PV = nRT


    P is the pressure

    V is the volume

    T is the temperature (in Kelvin)

    n is the amount of the gas

    R is the ideal gas constant

    Since R is constant, it will cancel out.  we are then given three values in "State 1" so we can solve for the remaining unknown.

    Then we can use that to find the unknown in "State 2".

    Using the P, V, and T that we are given, converting temperature to Kelvin, we can solve for "n" in terms of "R":

    K = C + 273.15

    K = 25 + 273.15

    K = 298.15

    PV = nRT

    950(75.0) = nR(298.15)

    71250 = nR(298.15)

    71250 / (298.15R) = n

    238.97367 / R = n

    (rounded to 5DP)

    Now we can use that value of "n" with the P and T in "State 2" to solve for the unknown V.  The "R"s should now cancel out:

    PV = nRT

    PV = (238.97367 / R)R(298)

    I didn't susbtitute the "P" yet as I noticed the different labels, so we'll have to convert that to torr, but first I'll simplify the above:

    PV = 238.97367(298)

    PV = 71214.15366

    We have 2.50 atm and need to convert it to torr since torr measurement was used in "Stage 1".  Google search gives me this conversion:

    760 torr/atm

    So 2.50 atm converted to torr is:

    2.50 atm (760 torr/atm) = 1900 torr

    We can now use this in P and solve for V:

    PV = 71214.15366

    1900V = 71214.15366

    V = 71214.15366 / 1900

    V = 37.48 L (rounded to 2DP)

    The new pressure more than double with a temperature decrease, which both would decrease volume, so this answer makes sense.

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