活性化エネルギーと触媒Activation Energy and Catalysts

1予想しよう（触る前に）Predict (before you touch anything)

1. 触媒を加えると、エネルギー図のどこが変わると思いますか。山の高さ、反応物の高さ、生成物の高さのそれぞれについて考えましょう。When a catalyst is added, what do you think changes on the energy diagram? Think about the height of the hill, the reactants and the products.💡 触媒は反応の前後で変化せず、反応物と生成物そのものは同じ物質です。A catalyst is unchanged at the end of the reaction, and the reactants and products are the same substances as before.
2. 温度を600 Kから300 Kに下げると、山を越えて生成物側に行くボールの数はどうなると思いますか。If the temperature is lowered from 600 K to 300 K, what do you think happens to the number of balls that get over the hill to the product side?💡 ボールの跳ねの高さは温度によって決まります。How high the balls hop depends on the temperature.

2動かしてみようTry it

1. 初期状態(温度 T=600 K、Ea=120 kJ/mol、ΔH=−40 kJ/mol、触媒OFF)で、左の谷のボールが跳ねて山に挑戦し、越えたボールが紫になって右の谷で緑になる様子を見る。図のEa・Ea'・ΔHの矢印と、右側の「k =」「累積到達」を読む。At the start (Temp. T = 600 K, Ea = 120 kJ/mol, ΔH = −40 kJ/mol, catalyst off), watch the balls in the left valley hop up the hill; those that cross turn purple and then green in the right valley. Read the Ea, Ea' and ΔH arrows on the diagram and "k =" and "Reached products" on the right.
2. 温度スライダーを300 K、1000 Kに変え、そのつど「リセット」を押して約10秒間の「累積到達」とkの値を記録する。Set the temperature slider to 300 K and then 1000 K, press "Reset" each time, and record "Reached products" after about 10 seconds and the value of k.
3. 600 Kに戻して「触媒 ON」にチェックを入れる。オレンジの点線の経路、「触媒 Ea=」の値、ΔHの矢印、kの値を触媒OFFのときと比べ、「リセット」して約10秒間の到達数も記録する。Return to 600 K and tick "Catalyst ON". Compare the dashed orange path, the "Catalyst Ea=" value, the ΔH arrow and k with the catalyst-off case, then press "Reset" and record the number reached in about 10 seconds.
4. ΔHスライダーを+30 kJ/molにして吸熱反応にし、生成物の谷の位置とEa、逆反応障壁Ea'の表示がどう変わるか確かめる。Move the ΔH slider to +30 kJ/mol to make the reaction endothermic, and check how the product valley, Ea and the reverse barrier Ea' change.
5. 下のk–Tグラフで、Ea=50とEa=200のときの曲線の傾きの違いを見る(Eaスライダーを動かして紫の曲線を比べる)。On the k vs T graph below, compare how steep the curve is for Ea = 50 and Ea = 200 (move the Ea slider and compare the purple curve).

3確かめようCheck

1. Ea=120 kJ/mol・触媒OFFで、300 K、600 K、1000 Kのkと約10秒間の到達数はどうでしたか。With Ea = 120 kJ/mol and no catalyst, what were k and the number reached in about 10 seconds at 300 K, 600 K and 1000 K?→ kは300 Kで1.27×10⁻⁸ s⁻¹、600 Kで3.57×10² s⁻¹、1000 Kで5.39×10⁶ s⁻¹。到達数は観察例で300 Kが0個、600 Kが5個前後、1000 Kが13個前後で、温度が高いほど増えた(ランダムなので回ごとに少し変わる)。k was 1.27×10⁻⁸ s⁻¹ at 300 K, 3.57×10² s⁻¹ at 600 K and 5.39×10⁶ s⁻¹ at 1000 K. In one run about 0 balls reached products at 300 K, about 5 at 600 K and about 13 at 1000 K: more at higher temperature (the counts vary a little each run because they are random).
2. 触媒をONにすると、何が変わり、何が変わりませんでしたか。When the catalyst was turned on, what changed and what did not?→ 障壁が120 kJ/molから72 kJ/mol(60%)に下がり、600 Kでkは3.57×10²から5.39×10⁶ s⁻¹へ約1万5千倍になり、到達数も増えた。反応物と生成物の谷の高さ(ΔH=−40 kJ/mol)は変わらなかった。The barrier dropped from 120 kJ/mol to 72 kJ/mol (60%), k at 600 K rose from 3.57×10² to 5.39×10⁶ s⁻¹ (about 15,000 times), and more balls reached the products. The heights of the reactant and product valleys (ΔH = −40 kJ/mol) did not change.
3. ΔH=−40 kJ/molと+30 kJ/molのとき、逆反応障壁Ea'はいくつでしたか。どんな関係がありますか。What was the reverse barrier Ea' for ΔH = −40 kJ/mol and +30 kJ/mol? What is the relationship?→ Ea=120 kJ/molのとき、ΔH=−40で160 kJ/mol、ΔH=+30で90 kJ/mol。Ea'=Ea−ΔHの関係があり、Ea(反応物の谷から峰まで)はΔHを変えても変わらない。With Ea = 120 kJ/mol, Ea' was 160 kJ/mol for ΔH = −40 and 90 kJ/mol for ΔH = +30. They follow Ea' = Ea − ΔH; Ea (from the reactant valley to the peak) does not change when ΔH changes.
4. k–Tグラフで、Eaが大きいほど曲線はどうなっていましたか。On the k vs T graph, how did the curve change as Ea became larger?→ Eaが大きいほど曲線は全体に下がり、傾きが急になった。Eaが大きい反応ほど低温ではほとんど進まず、温度による変化が大きい。The larger Ea, the lower the whole curve and the steeper it became. Reactions with a large Ea hardly proceed at low temperature and are more sensitive to temperature.

4考えようThink further

1. 触媒を使っても、反応で出入りする熱の量(反応熱)が変わらないのはなぜでしょうか。Why does using a catalyst not change the amount of heat released or absorbed (the enthalpy change)?→ 反応熱は反応物と生成物のエネルギーの差で決まり、途中の経路には関係しないから。触媒は途中の山(経路)だけを低くし、谷の高さは変えない(シミュレーションでもΔHの矢印は変わらない)。Because the enthalpy change depends only on the energy difference between reactants and products, not on the path between them. A catalyst lowers only the hill (the path), not the valleys (the ΔH arrow stays the same in the simulation).
2. Ea=60 kJ/mol・300 KとEa=120 kJ/mol・600 Kでは、kが同じ3.57×10² s⁻¹になります。なぜでしょうか。k is the same, 3.57×10² s⁻¹, for Ea = 60 kJ/mol at 300 K and for Ea = 120 kJ/mol at 600 K. Why?→ k = A·exp(−Ea/RT)はEaとTの比(Ea/RT)で決まり、両方ともEa/RTが同じだから。障壁が2倍でも温度が2倍なら越える割合は同じになる。Because k = A·exp(−Ea/RT) depends on the ratio Ea/RT, and both cases have the same Ea/RT. A barrier twice as high is crossed equally often when the temperature is also twice as high.

よくある誤解Common misconceptions

• 「触媒は反応熱を小さくしたり、生成物のエネルギーを変えたりする」という誤解。触媒が変えるのは活性化エネルギー(経路)だけで、ΔHは変わらない。"A catalyst reduces the heat of reaction or changes the energy of the products." A catalyst changes only the activation energy (the path); ΔH stays the same.
• 「発熱反応は活性化エネルギーが小さく、速く進む」という誤解。EaとΔHは別々の量で、発熱反応でもEaが大きければ低温ではほとんど進まない。"Exothermic reactions have small activation energies and go fast." Ea and ΔH are separate quantities; an exothermic reaction with a large Ea hardly proceeds at low temperature.

用語（日本語 / English）Key terms (Japanese / English)