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Pertanyaan

Tekanan gas O subscript 2 dalam suatu ruang adalah 101 kPa dan volume gas 22,4 L, banyak gas dalam ruang itu 1 mol. Berapakah kecepatan rata-rata molekul gas? Berapakah suhu gas?

R. Anjasmara

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

kecepatan rata-rata molekul gas adalah 460 m/s dan suhu gas adalah 272,25 K.

Pembahasan

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row n equals cell 1 space mol end cell row V equals cell 22 comma 4 space straight L equals 22 comma 4 cross times 10 to the power of negative 3 end exponent space straight m cubed end cell row P equals cell 101 space kPa equals 101 cross times 10 cubed space Pa end cell row cell M r subscript straight O subscript 2 end subscript end cell equals cell 32 space straight g divided by mol end cell row R equals cell 8 comma 31 space straight J divided by mol. straight K end cell end table 

Ditanyakan:

Kecepatan rata-rata molekul gas? Suhu gas?

Penyelesaian:

Massa gas O subscript 2 dihitung menggunakan persamaan jumlah mol gas.

table attributes columnalign right center left columnspacing 0px end attributes row n equals cell fraction numerator m over denominator M r end fraction end cell row m equals cell n M r end cell row blank equals cell 1 open parentheses 32 close parentheses end cell row blank equals cell 32 space straight g end cell row blank equals cell 32 cross times 10 to the power of negative 3 end exponent space kg end cell end table 

kecepatan rata-rata molekul gas berhubungan dengan tekanan, volume, dan massa gas. Dirumuskan persamaan;

table attributes columnalign right center left columnspacing 0px end attributes row cell v subscript r m s end subscript end cell equals cell square root of fraction numerator 3 P V over denominator m end fraction end root end cell row blank equals cell square root of fraction numerator 3 open parentheses 101 cross times 10 cubed close parentheses open parentheses 22 comma 4 cross times 10 to the power of negative 3 end exponent close parentheses over denominator 32 cross times 10 to the power of negative 3 end exponent end fraction end root end cell row blank equals cell square root of fraction numerator 6787 comma 2 over denominator 32 cross times 10 to the power of negative 3 end exponent end fraction end root end cell row blank equals cell square root of 21 comma 21 cross times 10 to the power of 4 end root end cell row blank equals cell 4 comma 6 cross times 10 squared space straight m divided by straight s end cell row blank equals cell 460 space straight m divided by straight s end cell end table 

Berdasarkan kecepatan rata-rata molekul gas ideal di atas, dan berdasarkan persamaan gas ideal P V equals n R T, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell v subscript r m s end subscript end cell equals cell square root of fraction numerator 3 P V over denominator m end fraction end root end cell row blank equals cell square root of fraction numerator 3 n R T over denominator m end fraction end root end cell row cell open parentheses v subscript r m s end subscript close parentheses squared end cell equals cell fraction numerator 3 n R T over denominator m end fraction end cell row T equals cell fraction numerator open parentheses v subscript r m s end subscript close parentheses squared m over denominator 3 n R end fraction end cell row blank equals cell fraction numerator open parentheses 4 comma 6 cross times 10 squared close parentheses squared open parentheses 32 cross times 10 to the power of negative 3 end exponent close parentheses over denominator 3 open parentheses 1 close parentheses open parentheses 8 comma 31 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 21 comma 21 cross times 10 to the power of 4 close parentheses open parentheses 32 cross times 10 to the power of negative 3 end exponent close parentheses over denominator 24 comma 93 end fraction end cell row blank equals cell fraction numerator 6787 comma 2 over denominator 24 comma 93 end fraction end cell row blank equals cell 272 comma 25 space straight K end cell end table 

Dengan demikian, kecepatan rata-rata molekul gas adalah 460 m/s dan suhu gas adalah 272,25 K.

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